Towards a sheaf cohomology theory for C*-algebras
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Martin Mathieu
Abstract
In jointwork with Pere Ara (Barcelona)we are in the process of developing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operatormodule sheaves over sheaves of C*-algebras are non-abelian and therefore the homology theory needed has to be set in the more general framework of exact categories.
Abstract
In jointwork with Pere Ara (Barcelona)we are in the process of developing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operatormodule sheaves over sheaves of C*-algebras are non-abelian and therefore the homology theory needed has to be set in the more general framework of exact categories.
Kapitel in diesem Buch
- Frontmatter i
- Dedication v
- Preface vi
- Contents ix
- Beurling’s Theorem on locally compact abelian groups 1
- Fréchet algebras with a dominating Hilbert algebra norm 5
- Relations between ideals of the Figà-Talamanca Herz algebra Ap(G) of a locally compact group G and ideals of Ap(H) of a closed subgroup 35
- The composition of conditional expectation and multiplication operators 47
- On the generation of Arveson weakly continuous semigroups 57
- ℓ1-bases in Banach algebras and Arens irregularities in harmonic analysis 95
- On spectral synthesis in convolution Sobolev algebras on the real line 133
- Projective and free matricially normed spaces 151
- Banach spaces whose algebras of operators are Dedekind-finite but they do not have stable rank one 165
- Invariant Complementation Property and Fixed Point Sets On Power Bounded Elements in the Group von Neumann Algebra 177
- Subspaces that can and cannot be the kernel of a bounded operator on a Banach space 189
- Towards a sheaf cohomology theory for C*-algebras 197
- Tame functionals on Banach algebras 213
- Left Ideals of Banach Algebras and Dual Banach Algebras 227
Kapitel in diesem Buch
- Frontmatter i
- Dedication v
- Preface vi
- Contents ix
- Beurling’s Theorem on locally compact abelian groups 1
- Fréchet algebras with a dominating Hilbert algebra norm 5
- Relations between ideals of the Figà-Talamanca Herz algebra Ap(G) of a locally compact group G and ideals of Ap(H) of a closed subgroup 35
- The composition of conditional expectation and multiplication operators 47
- On the generation of Arveson weakly continuous semigroups 57
- ℓ1-bases in Banach algebras and Arens irregularities in harmonic analysis 95
- On spectral synthesis in convolution Sobolev algebras on the real line 133
- Projective and free matricially normed spaces 151
- Banach spaces whose algebras of operators are Dedekind-finite but they do not have stable rank one 165
- Invariant Complementation Property and Fixed Point Sets On Power Bounded Elements in the Group von Neumann Algebra 177
- Subspaces that can and cannot be the kernel of a bounded operator on a Banach space 189
- Towards a sheaf cohomology theory for C*-algebras 197
- Tame functionals on Banach algebras 213
- Left Ideals of Banach Algebras and Dual Banach Algebras 227
