Title of article :
ON PSEUDO-CONTRACTIBILITY OF CERTAIN ALGEBRAS RELATED TO A DISCRETE SEMIGROUP
Author/Authors :
Sahami, Amir Department of Mathematics - Faculty of Basic Sciences - Ilam University - Ilam, Iran , Rostami, Mehdi Faculty of Mathematics and Computer Science Amirkabir University of Technology 424 Hafez Avenue - Tehran, Iran , Kalantari, Shahab Department of Basic Science Babol Noshirvani University of Technology - Shariati Avenue - Babol, Iran
Abstract :
In this paper, we introduce a notion of ultra central approximate identity for
Banach algebras which is a generalization of the bounded approximate identity and the central
approximate identity. Using this concept we study pseudo-contractibility of some matrix
algebras among ℓ1-Munn algebras. As an application, for the Brandt semigroup S = M0(G, I)
over a non-empty set I, we show that ℓ1(S) has an ultra central approximate identity if and
only if I is nite. Also we show that the notion of pseudo-contractibility and contractibility
are the same on ℓ1(S)
**
, where S is the Brandt semigroup.
Keywords :
Semigroup algebras , Ultra central approximate identity , Matrix algebras , Pseudo contractibility
Journal title :
Journal of Algebraic Structures and Their Applications
