Generalized Anderson's inequality

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:263

Article

Turnsek, A

关键词: normal operator;    norm inequality;    unitarily invariant norm;    von Neumann-Schatten class;   

DOI  :  10.1006/jmaa.2001.7602

来源: Elsevier

【 摘 要 】

Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of operators on H into itself. We study the elementary operator Phi: B(H) --> B(H) defined by Phi (X) = AXB - CXD, where A and C (respectively, B and D) are nonzero normal commuting operators. We prove that (i) parallel to Phi (X) + S parallel to greater than or equal to parallel toS parallel to for all S epsilon N(Phi) (the kernel of Phi) and for all X epsilon B(H) or (ii) parallel to Phi (X) + S parallel to (p) greater than or equal to parallel toS parallel to (p) for all S epsilon N(Phi) boolean AND C-p. (the van Neumann-Schatten ten class), 1 less than or equal to p < infinity p not equal 2, and for all X epsilon B(H) such that Phi (X) epsilon C-p if and only if N(A) boolean AND N(C) = X(B *) boolean AND N(D*) = {0}. (C) 2001 Academic Press.

【 授权许可】

Free