arXiv math/05010152005-01math.FA

Approximately Vanishing of Topological Cohomology Groups

Mohammad Sal Moslehian

备注：: 18 pages, minor corrections
发表信息：: J. Math. Anal. Appl. 318 (2006), no.2, 758-771
DOI：: 10.1016/j.jmaa.2005.06.018

英文摘要：

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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