Bounded Hochschild cohomology of Banach algebras with a matrix-like structure

Author:
Niels Grønbæk

Journal:
Trans. Amer. Math. Soc. **358** (2006), 2651-2662

MSC (2000):
Primary 46M20; Secondary 47B07, 16E40

DOI:
https://doi.org/10.1090/S0002-9947-06-03913-4

Published electronically:
January 24, 2006

MathSciNet review:
2204050

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Abstract: Let be a unital Banach algebra. A projection in which is equivalent to the identitity may give rise to a matrix-like structure on any two-sided ideal in . In this set-up we prove a theorem to the effect that the bounded cohomology vanishes for all . The hypotheses of this theorem involve (i) strong H-unitality of , (ii) a growth condition on diagonal matrices in , and (iii) an extension of in by an amenable Banach algebra. As a corollary we show that if is an infinite dimensional Banach space with the bounded approximation property, is an infinite dimensional -space, and is the Banach algebra of approximable operators on , then for all .

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Additional Information

**Niels Grønbæk**

Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Email:
gronbaek@math.ku.dk

DOI:
https://doi.org/10.1090/S0002-9947-06-03913-4

Keywords:
Bounded Hochschild cohomology,
H-unital,
simplicially trivial

Received by editor(s):
December 2, 2003

Received by editor(s) in revised form:
August 3, 2004

Published electronically:
January 24, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.