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A Note on Subnormal and Hyponormal Derivations

2008
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Kyungpook Mathematical Journal
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In this note we prove that if A and B * are subnormal operators and X 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 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 X ∈ L(H) is such that SX − XT belongs to a norm ideal (J, || · ||J ) and prove that f (S)X − Xf (T ) ∈ J and ||f (S)X − Xf (T )||J ≤ C ||SX − XT ||J , for f in a certain class of functions.

doi:10.5666/kmj.2008.48.2.281
fatcat:kouszsb6hngjvdgvnnxmioeeqi