A Note on the Range of the Operator ð ‘‹ ↦ 𠑇 ð ‘‹ − ð ‘‹ 𠑇 Defined on ð ’ž 2 ( â„‹ )

Vasile Lauric

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-6

Abstract:

We show how a proof of J. Stampfli can be extended to prove that the operator ð ‘‹ ↦ 𠑇 ð ‘‹ − ð ‘‹ 𠑇 defined on the Hilbert-Schmidt class, when 𠑇 is an ð ‘€ -hyponormal, ð ‘ -hyponormal, or log-hyponormal operator, has a closed range if and only if 𠜎 ( 𠑇 ) is finite.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:603041

DOI: 10.1155/2009/603041

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