A Cohomological Property of π-invariant Elements
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Published:2013-09-01
Issue:3
Volume:56
Page:534-543
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Author:
Filali M.,Sangani Monfared M.
Abstract
Abstract.Let A be a Banach algebra and let be a continuous representation of A on a separable Hilbert space H with dim H = m. Let πi j be the coordinate functions of π with respect to an orthonormal basis and suppose that for each and . Under these conditions, we call an element left π-invariant if In this paper we prove a link between the existence of left π-invariant elements and the vanishing of certain Hochschild cohomology groups of A. Our results extend an earlier result by Lau on F-algebras and recent results of Kaniuth, Lau, Pym, and and the second author in the special case where π : A → C is a non-zero character on A.
Publisher
Canadian Mathematical Society
Subject
General Mathematics