The projection calculus

The projection calculus

We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for C*-algebras of real rank zero, specifically on liftings, excising...

Verfasser:	Bice, Tristan
Dokumenttypen:	Artikel
Erscheinungsdatum:	2013
Publikation in MIAMI:	05.05.2014
Datum der letzten Änderung:	28.04.2022
Quelle:	Münster Journal of Mathematics, 6 (2013), S. 557-581
Angaben zur Ausgabe:	[Electronic ed.]
Fachgebiet (DDC):	510: Mathematik
Lizenz:	InC 1.0
Sprache:	Englisch
Format:	PDF-Dokument
URN:	urn:nbn:de:hbz:6-55309456861
Permalink:	https://nbn-resolving.de/urn:nbn:de:hbz:6-55309456861
Onlinezugriff:	MJM_2013_6_557-581.pdf

Münster Journal of Mathematics

1 (2008), S. 1-8: Eulerian polynomials of spherical type
1 (2008), S. 9-14: Eulerian polynomials
1 (2008), S. 15-72: Matrix-valued random walks and variations on property AT
1 (2008), S. 73-108: Survey on geometric group theory
1 (2008), S. 109-142: Splitting polytopes
1 (2008), S. 143-180: L²-Betti numbers of coamenable quantum groups
1 (2008), S. 181-220: The unitary character group of abelian unipotent groups
1 (2008), S. 221-236: Projective C*-algebras and boundary maps
1 (2008), S. 237-266: Isomorphisms in ℓ¹-homology
1 (2008), S. 267-278: A note on Banach C₀(X)-modules
2 (2009), S. 3-4: Editorial Münster Journal of Mathematics / 2 (2009)
2 (2009), S. 5-34: K-theory of Leavitt path algebras
2 (2009), S. 35-44: Strongly self-absorbing C*-algebras which contain a nontrivial projection
2 (2009), S. 45-64: Mahler measures and Fuglede-Kadison determinants
2 (2009), S. 65-94: Equivariant K-theory of finite dimensional real vector spaces
2 (2009), S. 95-142: Ocneanu cells and Boltzmann weights for the SU(3) ADE graphs
2 (2009), S. 143-182: An enrichment of KK-theory over the category of symmetric spectra
2 (2009), S. 183-200: Skew Hopf algebras, irreducible extensions and the Π-method
2 (2009), S. 201-214: On the classifying space of the family of virtually cyclic subgroups for CAT(0...
2 (2009), S. 215-252: C*-algebras over topological spaces the bootstrap class
2 (2009), S. 253-264: Die universelle beschränkte Derivation
2 (2009), S. 265-298: Dirac operators for coadjoint orbits of compact Lie groups
2 (2009), S. 299-310: Duality of cones of positive maps
2 (2009), S. 311-324: Completely positive maps of order zero
3 (2010), S. 1-10: Homology and cohomology theories on manifolds
3 (2010), S. 11-28: Ideals and simplicity of crossed products of graph C*-algebras by quasi-free act...
3 (2010), S. 29-42: Representations attached to vector bundles on curves over finite and p-adic fiel...
3 (2010), S. 43-66: Computable functions of reals
3 (2010), S. 67-88: Detecting orbits along subvarieties via the moment map
3 (2010), S. 89-110: Doubloons and q-secant numbers
3 (2010), S. 111-144: A dynamical core for topological directed graphs
3 (2010), S. 145-162: Acyclic chain complexes over the orbit category
3 (2010), S. 163-212: Double martingale structure and existence of φ-moments for weighted branching...
3 (2010), S. 213-220: Excellence of G₂ and F₄
3 (2010), S. 221-232: The icosahedral group and the homotopy of the stable mapping class group
3 (2010), S. 233-236: On the action of the group of isometries on a locally compact metric space
3 (2010), S. 237-262: The ideal structure of reduced crossed products
3 (2010), S. 263-272: Classifying spaces for proper actions of mapping class groups
4 (2011), S. 1-28: Branching of representations to symmetric subgroups
4 (2011), S. 29-52: Smooth and rough modules over self-induced algebras
4 (2011), S. 53-64: Alexandrov meets Lott-Villani-Sturm
4 (2011), S. 65-72: Nuclear dimension and n-comparison
4 (2011), S. 73-100: Multiplier algebras of C₀(X)-algebras
4 (2011), S. 101-118: Free products of sofic groups with amalgamation over monotileably amenable gro...
4 (2011), S. 119-128: On the zeroth L²-homology of a quantum group
4 (2011), S. 129-140: An improvement of de Jong-Oort’s purity theorem
4 (2011), S. 141-170: Almost one-to-one extensions of Cantor minimal systems and order embeddings of...
4 (2011), S. 171-184: Zeta functions and topological entropy of the Markov-Dyck shifts
4 (2011), S. 185-226: On the reduction of the Siegel moduli space of abelian varieties of dimension ...
4 (2011), S. 227-250: Groupoid cocycles and K-theory
5 (2012), S. 1-24: Homomorphisms of quantum groups
5 (2012), S. 25-40: Riemannian submersions from simple, compact Lie groups
5 (2012), S. 41-58: On the Bateman-Horn Conjecture about polynomial rings
5 (2012), S. 59-72: The Takesaki equivalence relation for maximal abelian subalgebras
5 (2012), S. 73-98: Free group actions from the viewpoint of dynamical systems
5 (2012), S. 99-106: On transverse triangulations
5 (2012), S. 107-120: The Euler ring of the rotation group
5 (2012), S. 121-150: Amplified graph C*-algebras
5 (2012), S. 151-182: Cuntz-Li relations, inverse semigroups and groupoids
5 (2012), S. 183-208: On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity
5 (2012), S. 209-232: Inner coactions, Fell bundles, and abstract uniqueness theorems
5 (2012), S. 233-248: Separable and tree-like asymptotic cones of groups
6 (2013), S. 1-51: The group of automorphisms of the algebra of one-sided inverses of a polynomial a...
6 (2013), S. 53-83: Fell bundles and imprimitivity theorems
6 (2013), S. 85-116: Euler characteristics of categories and barycentric subdivision
6 (2013), S. 117-166: The extender algebra and vagaries of Σ^2_1 absoluteness
6 (2013), S. 167-179: Connes–Karoubi long exact sequence for Fréchet sheaves
6 (2013), S. 181-269: The total surgery obstruction revisited
6 (2013), S. 271-294: An analogue of Raynaud’s theorem weak formal schemes and dagger spaces
6 (2013), S. 295-341: Generalized fixed point algebras for coactions of locally compact quantum grou...
6 (2013), S. 343-364: Families index for Boutet de Monvel operators
6 (2013), S. 365-382: Axiomatic homology and duality revisited
6 (2013), S. 383-411: Representations of C*-dynamical systems implemented by Cuntz families
6 (2013), S. 413-444: Localization techniques in circle-equivariant Kasparov theory
6 (2013), S. 445-482: Completely bounded representations of convolution algebras of locally compact ...
6 (2013), S. 483-523: Topology of the octonionic flag manifold
6 (2013), S. 525-554: How to recognize a 4-ball when you see one
6 (2013), S. 555-556: Erratum to: How to recognize a 4-ball when you see one
6 (2013), S. 557-581: The projection calculus
6 (2013), S. 583-594: Z-stability, finite dimensional tracial boundaries and continuous rank functio...
7 (2014) 1, S. 3: Editorial Münster Journal of Mathematics / 7 (2014)
7 (2014) 1, S. 5-26: Verma modules for Iwasawa algebras are faithful
7 (2014) 1, S. 27-50: On the local Langlands correspondence for non-tempered representations
7 (2014) 1, S. 51-81: Relative continuous K-theory and cyclic homology
7 (2014) 1, S. 83-103: On the 2-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves w...
7 (2014) 1, S. 105-114: An alternative to Witt vectors
7 (2014) 1, S. 115-134: Locally unitary principal series representations of GLd+1(F)
7 (2014) 1, S. 135-148: A spectral sequence for Iwasawa adjoints
7 (2014) 1, S. 149-223: Refined Iwasawa theory for p-adic representations and the structure of Selme...
7 (2014) 1, S. 225-240: Resolutions for principal series representations of p-adic GLn
7 (2014) 1, S. 241-271: Integral models of ℙ¹ and analytic distribution algebras for GL(2)
7 (2014) 1, S. 273-326: Towards a theory of local Shimura varieties
7 (2014) 1, S. 327-343: Euler characteristic and congruences of elliptic curves
7 (2014) 1, S. 345-362: A note on determinant functors and spectral sequences
7 (2014) 1, S. 363-379: The pro-p-Iwahori–Hecke algebra of a reductive p-adic group, II
7 (2014) 2, S. 381-412: Finite symmetry group actions on substitution tiling C*-algebras
7 (2014) 2, S. 413-437: Duality theory for nonergodic actions
7 (2014) 2, S. 439-462: Fixed points for actions of Aut(Fn) on CAT(0) spaces
7 (2014) 2, S. 463-487: On convex hulls of orbits of Coxeter groups and Weyl groups
7 (2014) 2, S. 489-514: A class of C*-algebras that are prime but not primitive
7 (2014) 2, S. 515-528: A simple C*-algebra with finite nuclear dimension which is not Z-stable
7 (2014) 2, S. 529-556: Bruhat strata and F-zips with additional structure
7 (2014) 2, S. 557-588: Non-embeddable polar spaces
7 (2014) 2, S. 589-607: Equivariant K-homology of Bianchi groups in the case of nontrivial class gro...
7 (2014) 2, S. 609-621: On groups and fields interpretable in torsion-free hyperbolic groups
7 (2014) 2, S. 623-670: Local P-shtukas and their relation to global G-shtukas
7 (2014) 2, S. 671-696: Quillen property of real algebraic varieties
7 (2014) 2, S. 697-729: R/Z-valued index theory via geometric K-homology
7 (2014) 2, S. 731-752: On rates of convergence for the overlap in the Hopfield model
7 (2014) 2, S. 753-769: Nonabelian symmetries of quasitoric manifolds
8 (2015), S. 1-16: Riemannian foliations on contractible manifolds
8 (2015), S. 17-22: Continuous fields of C*-algebras and quasidiagonality
8 (2015), S. 23-56: Exact C*-algebras and C0(X)-structure
8 (2015), S. 57-98: Convergence of fuzzy tori and quantum tori for the quantum Gromov–Hausdorff pr...
8 (2015), S. 99-117: Groups with twisted p-periodic cohomology
8 (2015), S. 119-167: Cobordism category of manifolds with Baas–Sullivan singularities
8 (2015), S. 169-179: The de Rham cohomology of Drinfeld’s half space
8 (2015), S. 181-210: Generalized spin representations
8 (2015), S. 211-228: Conformally Kähler geometry and quasi-Einstein metrics
8 (2015), S. 229-239: On flow-equivalence of R-graph shifts
8 (2015), S. 241-252: A non-amenable groupoid whose maximal and reduced C*-algebras are the same
8 (2015), S. 253-284: Quantum isometries of noncommutative polygonal spheres
9 (2016), S. 1-34: Irreducible affine isometric actions on Hilbert spaces
9 (2016), S. 35-50: On homogeneous composed Clifford foliations
9 (2016), S. 51-76: Colimits in the correspondence bicategory
9 (2016), S. 77-91: Homology of group von Neumann algebras
9 (2016), S. 93-118: Conjugacy and cocycle conjugacy of automorphisms of O2 are not Borel
9 (2016), S. 119: Erratum to: The pro-p-Iwahori–Hecke algebra of a reductive p-adic group, II
9 (2016), S. 121-154: Sums of commutators in pure C*-algebras
9 (2016), S. 155-185: C*-algebras associated to topological Ore semigroups
9 (2016), S. 187-206: Nonnegative curvature, low cohomogeneity and complex cohomology
9 (2016), S. 207-219: Analytic filling of totally real tori
9 (2016), S. 221-251: Graph Laplacians, component groups and Drinfeld modular curves
9 (2016), S. 253-261: Irreducible representations of nilpotent groups generate classifiable C*-algeb...
10 (2017), S. 1-17: Singularities and Quinn spectra
10 (2017), S. 19-37: Structural properties of close II1 factors
10 (2017), S. 39-58: Functoriality and K-theory for GLn(R)
10 (2017), S. 59-74: Equivariant correspondences and the Borel–Bott–Weil theorem
10 (2017), S. 75-81: The Grothendieck group of polytopes and norms
10 (2017), S. 83-118: Descent properties of topological chiral homology
10 (2017), S. 119-129: A remark on the isomorphism conjectures
10 (2017), S. 131-170: Gap distributions in circle packings
10 (2017), S. 171-188: A geometric description of the Atiyah–Hirzebruch spectral sequence for B-bo...
10 (2017), S. 189-200: Nontrivial homeomorphisms of Čech– Stone remainders
10 (2017), S. 201-268: Persistence approximation property and controlled operator K-theory
10 (2017), S. 269-275: Axiomatizability of the stable rank of C*-algebras
10 (2017), S. 277-286: On rigidity of locally symmetric spaces
10 (2017), S. 287-365: Convergence to the boundary for random walks on discrete quantum groups and m...
10 (2017), S. 367-381: Cartan subalgebras of topological graph algebras and k-graph C*-algebras
10 (2017), S. 383-407: A real Jiang–Su algebra
10 (2017), S. 409-424: Obstructions to lifting cocycles on groupoids and the associated C*-algebras
10 (2017), S. 425-455: Lecture notes on stabilization of contact open books
10 (2017), S. 457-483: Complex analogues of the half-classical geometry
10 (2017), S. 485-521: The real C*-algebra of a graph with involution
11 (2018), S. 1-12: Non-commutative twisted Euler characteristic
11 (2018), S. 13-47: Theory of optimal transport for Lorentzian cost functions
11 (2018), S. 49-156: Invariants for permutation-Hermite equivalence and critical dimension groups
11 (2018), S. 157-209: Foliated manifolds, algebraic K-theory, and a secondary invariant
11 (2018), S. 211-216: AF-embeddings of residually finite-dimensional C*-algebras
11 (2018), S. 217-224: Kirchberg–Wassermann exactness vs exactness: reduction to the unimodular to...
12 (2019), S. 1-29: Horospherical stacks
12 (2019), S. 31-48: Symplectic dynamics of contact isotropic torus complements
12 (2019), S. 49-56: A combinatorial model for tame frieze patterns
12 (2019), S. 57-92: Relative geometric assembly and mapping cones Part II: Chern characters and the...
12 (2019), S. 93-137: Higher-rank graph algebras are iterated Cuntz–Pimsner algebras
12 (2019), S. 139-161: Composita of symmetric extensions of Q
12 (2019), S. 163-214: A proper mapping theorem for coadmissible D-modules
12 (2019), S. 215-237: Induction and restriction of (φ,Γ)-modules
12 (2019), S. 239-410: The term a4 in the heat kernel expansion of noncommutative tori
12 (2019), S. 411-451: Ample groupoids: Equivalence, homology, and Matui's HK conjecture
12 (2019), S. 453-471: Ping-pong in Hadamard manifolds
12 (2019), S. 473-495: Certain actions of finite abelian groups on higher dimensional noncommutative...
13 (2020), S. 1-114: Kac–Moody symmetric spaces
13 (2020), S. 115-143: CCR flows associated to closed convex cones
13 (2020), S. 145-196: Spectral theory in a twisted groupoid setting: Spectral decompositions, local...
13 (2020), S. 197-204: Decomposing nuclear maps
13 (2020), S. 205-218: The Curie–Weiss model—an approach using moments
13 (2020), S. 219-220: Editorial Münster Journal of Mathematics / 13 (2020) 2
13 (2020), S. 221-265: Analysis on Riemannian foliations of bounded geometry
13 (2020), S. 267-316: A p-adically entire function with integral values on Qp and entire liftings o...
13 (2020), S. 317-352: Diagonal classes and the Bloch–Kato conjecture
13 (2020), S. 353-424: Transfers in coarse homology
13 (2020), S. 425-444: Aspects of p-adic operator algebras
13 (2020), S. 445-507: On p-adic comparison theorems for rigid analytic varieties, I
13 (2020), S. 509-518: Extensions in the cohomology of Hilbert modular varieties
13 (2020), S. 519-540: Deninger’s conjectures and Weil–Arakelov cohomology
13 (2020), S. 541-571: Overconvergent de Rham–Witt cohomology for semi-stable varieties
13 (2020), S. 573-596: Galois theory of periods
13 (2020), S. 597-619: Some specialization theorems for families of abelian varieties
14 (2021), S. 1-40: Blow-up constructions for Lie groupoids and a Boutet de Monvel type calculus
14 (2021), S. 41-57: A tracially AF algebra which is not Z-absorbing
14 (2021), S. 59-99: Skew products of finitely aligned left cancellative small categories and Cuntz-...
14 (2021), S. 101-122: Hochschild cohomology and p-adic Lie groups
14 (2021), S. 123-154: On an index theorem of Chang, Weinberger and Yu
14 (2021), S. 155-163: The Weierstrass preparation theorem and resultants of p-adic power series
14 (2021), S. 165-189: Topological full groups of ultragraph groupoids as an isomorphism invariant
14 (2021), S. 191-221: Generating derived categories of groups in Kropholler's hierarchy.
14 (2021), S. 223-263: Fell bundles over quasi-lattice ordered groups and C*-algebras of compactly a...
14 (2021), S. 265-281: Classifying maps into uniform tracial sequence algebras
14 (2021), S. 283-293: Norm equivalences and ideals of composition algebras
14 (2021), S. 295-321: An Obata-type characterization of doubly-warped product Kähler manifolds
14 (2021), S. 323-348: On 3-dimensional foliated dynamical systems and Hilbert type reciprocity law
14 (2021), S. 349-402: An excision theorem for the K-theory of C*-algebras, with applications to gro...
14 (2021), S. 403-443: Fredholm conditions and index for restrictions of invariant pseudodifferentia...
14 (2021), S. 445-484: Projective geometry for perfectoid spaces
14 (2021), S. 485-496: Elements with north-south dynamics and free subgroups have positive density i...
14 (2021), S. 497-507: On R-triviality of F4, II
14 (2021), S. 509-536: An identification of the Baum-Connes and Davis-Lück assembly maps
14 (2021), S. 537-558: On the homotopy type of the spaces of spherical knots in Rn
14 (2021), S. 559-583: Classification of irrational Θ-deformed CAR C*-algebras
14 (2021), S. 585-606: Unitary Cuntz semigroups of ideals and quotients
15 (2022), S. 1-46: Connected algebraic groups acting on Fano fibrations over P¹
15 (2022), S. 47-81: Reducibility of low-dimensional Poincaré duality spaces
15 (2022), S. 83-166: On extension of rigid analytic objects
15 (2022), S. 167-220: The stable rank of diagonal ASH algebras and crossed products by minimal home...
15 (2022), S. 221-233: Random walk and Fibonacci matrices
15 (2022), S. 235-240: A strong Schottky lemma on n generators for CAT(0) spaces
15 (2022), S. 241-278: C*-algebras from partial isometric representations of LCM semigroups
15 (2022), S. 279-304: Continuous group cohomology and Ext-groups
15 (2022), S. 305-331: Index theorem for inhomogeneous hypoelliptic differential operators
15 (2022), S. 333-354: Full quantum crossed products, invariant measures, and type-I lifting
15 (2022), S. 355-388: Bordism and projective space bundles
15 (2022), S. 389-440: Holomorphic curves in the symplectizations of lens spaces: An elementary appr...
15 (2022), S. 441-471: Passing C*-correspondence relations to the Cuntz–Pimsner algebras
15 (2022), S. 473-498: Locally normal subgroups and ends of locally compact Kac–Moody groups
16 (2023), S. 1-24: Split extensions and KK-equivalences for quantum projective spaces
16 (2023), S. 25-50: Connes–Moscovici residue cocycle for some Dirac-type operators
16 (2023), S. 51-94: Complexity rank for C*-algebras
16 (2023), S. 95-145: Equivalence of Fell bundles is an equivalence relation
16 (2023), S. 147-175: Non-Hausdorff étale groupoids and C*-algebras of left cancellative monoids
16 (2023), S. 177-199: Invariants for the Smale space associated to an expanding endomorphism of a f...
16 (2023), S. 201-263: Spherical representations of C*-flows, I
16 (2023), S. 265-300: Local models, Mustafin varieties and semi-stable resolutions
16 (2023), S. 301-322: Ultraproducts of factorial W*-bundles
16 (2023), S. 323-487: Λ-buildings associated to quasi-split groups over Λ-valued fields
16 (2023), S. 489-490: Erratum to: Classifying maps into uniform tracial sequence algebras

The projection calculus

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