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

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  • Vasile Lauric

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.

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  • Vasile Lauric, 2009. "A Note on the Range of the Operator ð ‘‹ ↦ 𠑇 ð ‘‹ − ð ‘‹ 𠑇 Defined on ð ’ž 2 ( â„‹ )," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-6, July.
    • Handle: RePEc:hin:jijmms:603041
    DOI: 10.1155/2009/603041
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