Biamenability of Banach algebras and its applications

Document Type : Original Article

Authors

Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran

Abstract

In this paper, we introduce the concept of biamenability of Banach

algebras and we show that despite the apparent similarities between amenabil-

ity and biamenability of Banach algebras, they lead to very di erent, and

somewhat opposed, theories. In this regard, we show that commutative Ba-

nach algebras and the group algebra L1(G), for each locally compact group

G, tend to lack biamenability, while they may be amenable and highly non-

commutative Banach algebras such as B(H) for an in nite-dimensional Hilbert

space H tend to be biamenable, while they are not amenable. Also, we show

that although the unconditional unitization of an amenable Banach algebra is

amenable but in general unconditional unitization of a Banach algebra is not

biamenable.

This concept may be applied for studying the character space of some Ba-

nach algebras and also for studying some spansion or density problems.

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Main Subjects