On Cyclic Amenability of Triangular Banach Algebras

چکیده مقاله

ABSTRACT. The inherited properties between the triangular Banach algebra in the form of T =Tri [A, M, B] and the corner Banach algebras A and B are very important and studied. In this paper, first, a method for investigating being cyclic of derivations on Banach algebras is presented and then the cyclic derivations on triangular Banach algebras are studied. Using the above method, we show that the unital triangular Banach algebra T is cyclic amenable if and only if the corner algebras A and B are cyclic amenable. Finally, an example shows that the condition of unitary of T is necessary for the correctness of the results.