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Keywords

Elementary operator

Abstract

Let X be a complex Banach space and L(X) be the algebra of all bounded linear operators on X. For a given elementary operator P of length 2 on L(X), we determine necessary and sufficient conditions for the existence of a solution of the equation YP=0 in the algebra of all elementary operators on L(X). Our approach allows us to characterize some invertible elementary operators of length 2 whose inverses are elementary operators.

abs_vol30_pp916-933 (2).tex (3 kB)
Abstract

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