Some Estimates of Certain Subnormal and Hyponormal Derivations

Vasile Lauric

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-6

Abstract:

We prove that if ð ´ and ð µ âˆ— are subnormal operators and ð ‘‹ is a bounded linear operator such that ð ´ ð ‘‹ − ð ‘‹ ð µ is a Hilbert-Schmidt operator, then ð ‘“ ( ð ´ ) ð ‘‹ − ð ‘‹ ð ‘“ ( ð µ ) is also a Hilbert-Schmidt operator and ‖ ð ‘“ ( ð ´ ) ð ‘‹ − ð ‘‹ ð ‘“ ( ð µ ) ‖ 2 ≤ ð ¿ â€– ð ´ ð ‘‹ − ð ‘‹ ð µ â€– 2 for ð ‘“ belongs to a certain class of functions. Furthermore, we investigate the similar problem in the case that 𠑆 , 𠑇 are hyponormal operators and ð ‘‹ ∈ â„’ ( â„‹ ) is such that 𠑆 ð ‘‹ − ð ‘‹ 𠑇 belongs to a norm ideal ( ð ½ , ‖ â‹… ‖ ð ½ ) , and we prove that ð ‘“ ( 𠑆 ) ð ‘‹ − ð ‘‹ ð ‘“ ( 𠑇 ) ∈ ð ½ and ‖ ð ‘“ ( 𠑆 ) ð ‘‹ − ð ‘‹ ð ‘“ ( 𠑇 ) ‖ ð ½ â‰¤ ð ¶ â€– 𠑆 ð ‘‹ − ð ‘‹ 𠑇 ‖ ð ½ for ð ‘“ being in a certain class of functions.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:362409

DOI: 10.1155/2008/362409

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