A Note on Subnormal and Hyponormal Derivations

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 2,  2008, pp.281-286
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.2.281
Title & Authors
A Note on Subnormal and Hyponormal Derivations
Lauric, Vasile;

Abstract
In this note we prove that if A and $\small{B^*}$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $\small{{\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2}$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $\small{X\;{\in}\;\cal{L}(\cal{H})}$ is such that SX - XT belongs to a norm ideal (J, $\small{{\parallel}\;{\cdot}\;{\parallel}_J}$) and prove that f(S)X - Xf(T) $\small{\in}$ J and $\small{{\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J}$, for f in a certain class of functions.
Keywords
subnormal derivations;hyponormal derivations;
Language
English
Cited by
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