Perturbations of nonassociative Banach algebras
by
Anar Dosiev
Institute of Mathematics and Mechanics, Azerbaijan

We talk about the perturbation problem in the nonassociative Banach algebra context. The problem is the following. If we perturb the multiplication in a Banach algebra, do we obtain a topologically isomorphic algebra? For associative Banach algebras the problem is well known and serious advancements were done by B.E. Johnson, Perturbations of Banach algebras, Proc. London Math. Soc. (3) 34 (1977) 439-458, and I. Raeburn, J.L. Taylor, Hochschild cohomology and perturbations of Banach algebras, J. Funct. Anal. 25 (1977) 258-266, independently. We focus on Banach-Jordan and Banach-Lie algebras. Our approach is based on Implicit Function Theorem proposed by I. Raeburn and J.L. Taylor. Roughly speaking, by differentiating the identities of a nonassocitive Banach algebra we are raising on the cohomology level. By assuming certain cohomologies to be vanish we obtain the positive solution of the perturbation problem on the ground of Implicit Function Theorem.

Date received: May 19, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cane-32.