Article ID Journal Published Year Pages File Type
4621600 Journal of Mathematical Analysis and Applications 2008 7 Pages PDF
Abstract

Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero.

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Physical Sciences and Engineering Mathematics Analysis