A Note on Subnormal and Hyponormal Derivations

Vasile Lauric
2008 Kyungpook Mathematical Journal  
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