Vol. 84, No. 2, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Cohomology over Banach crossed products. Application to bounded derivations and crossed homomorphisms

Guy Loupias

Vol. 84 (1979), No. 2, 333–366
Abstract

The purpose of this work is to study the structure of bounded derivations and crossed homomorphisms of the Banach crossed product A = L1(G,A) of a Banach--algebra A acted upon by a locally compact group G. As bounded derivations and crossed homomorphisms are related to 1-cocycles, we first define and study cohomology over A, generalizing cohomology over group algebras. Then, if G is amenable and A is a C-algebra, or the dual of a Banach space, we show that a bounded derivation (resp. a crossed homomorphism) on A is equivalent to some couple of a bounded derivation (resp. a crossed homomorphism) from A to M1(G,A) and a bounded measure on A with value in the centralizers of A (resp. an element of A).

Mathematical Subject Classification 2000
Primary: 46M20
Secondary: 46K99, 46L05
Milestones
Received: 28 February 1978
Published: 1 October 1979
Authors
Guy Loupias