Vanishing of First (σ − Τ)-cohomology Group of Triangular Banach Algebras
نویسندگان
چکیده
; a ∈ A,m ∈ M, b ∈ B} equipped with the usual 2× 2 matrix-like addition and matrix-like multiplication is an algebra. An algebra T is called a triangular algebra if there exist algebras A and B and nonzero A−B-bimodule M such that T is (algebraically) isomorphic to Tri(A,M,B) under matrixlike addition and matrix-like multiplication; cf. [1]. For example, the algebra Tn of n × n upper triangular matrices over the complex field C, may be viewed as a triangular algebra when n > 1. In fact, if n > k, we have Tn = Tri(Tn−k,Mn−k,k(C), Tk) in which Mn−k,k(C) is the space of (n− k)× k complex matrices. Let T is a triangular algebra. If 1 = [
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