Approximately Vanishing of Topological Cohomology Groups

Details Approximately Vanishing of Topological Cohomology Groups Approximately Vanishing of Topological Cohomology Groups

2005-01-02

arxiv.org/abs/math/0501015v2

J. Math. Anal. Appl. 318 (2006), no.2, 758-771

Mathematics

Functional Analysis

18 pages, minor corrections

Scientific paper

In this paper, we establish the Pexiderized stability of coboundaries and
cocycles and use them to investigate the Hyers--Ulam stability of some
functional equations. We prove that for each Banach algebra $A$, Banach
$A$-bimodule $X$ and positive integer $n, H^n(A,X)=0$ if and only if the $n$-th
cohomology group approximately vanishes.

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