Derivations of triangular Banach algebras

Module character inner amenability of Banach algebras

“…The l 1 -direct sum of A and X, denoted by A È 1 X, with the product defined by This Banach algebra were introduced by Forrest and Marcoux in [7]. Note that s can be identified with the module extension ðA È 1 BÞ È 1 X, in which X is considered as a A È 1 B-module under the operations: ða; bÞ:x ¼ ax; x:ða; bÞ ¼ xbða 2 A; b 2 B; x 2 XÞ:…”

Weak amenability of triangular Banach algebras

“…In [7], motivated by work of Gilfeather and Smith [8] in their study of joins of operator algebras, we began an investigation of derivations of triangular Banach algebras; these are algebras of the form…”

“…Indeed, when n is odd, the (first) cohomology group of T depends only upon that of A and B [see Theorem 3.7 below]. When n is even, the techniques developed in [7] can be extended to this setting, where it allows us to compute H 1 (T , T (2n) ) for many choices of A, B and M [see Theorem 3.12].…”

On (Co)homology of triangular Banach algebras

“…algebras of the form T = [ A M 0 B ] in which A and B are unital Banach algebras and M is a unital Banach A, B-module. These algebras were introduced by Forrest and Marcoux [1], motivated by work of Gilfeather and Smith in [4]. Forrest and Marcoux also studied and directly computed some cohomology groups of triangular Banach algebras (see [2] and [3]).…”

“…These algebras were introduced by Forrest and Marcoux [1], motivated by work of Gilfeather and Smith in [4]. Forrest and Marcoux also studied and directly computed some cohomology groups of triangular Banach algebras (see [2] and [3]). In this paper, after some preliminaries, we present two long exact sequences and apply them to give some significant isomorphisms and vanishing theorems.…”