On the range of a generalized derivation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the range of a generalized derivation

Authors:	S. Mecheri

Affiliation:	(1) School of Mathematics, The University of New South Wales, Sydney, 2052, Australia;(2) Department of Mathematics, 333 Avery Hall, The University of Nebraska, Lincoln, Lincoln, NE 68588-0130, USA;(3) Department of Mathematics, Creighton University, Omaha, NE 68178, USA

Abstract:	A generalized derivation $delta _{{rm A},{rm B}} :mathcal{L}(mathcal{H}) mapsto mathcal{L}(mathcal{H})$ , is defined by the formula $delta _{{rm A},{rm B}} :(X) = AX - XB$ , where and is the Banach algebra of bounded linear operators in a Hilbert space . Sufficient conditions under which $overline {R(delta _{{rm A},{rm B}} )} cap kerdelta _{{rm A},{rm B}} = left{ 0 right}$ and $overline {R(delta _{{rm A},{rm B}} )} cap kerdelta _{{rm A}^ * ,{rm B}^ * } = left{ 0 right}$ are given. Bibliography: 8 titles. Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 111–119.

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