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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyponormal operators with infinite essential spectrum
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by Hong W. Kim PDF
Proc. Amer. Math. Soc. 51 (1975), 44-48 Request permission

Abstract:

It is shown that if $T$ is an essentially hyponormal operator (i.e., the image of ${T^ \ast }T - T{T^ \ast }$ in the Calkin algebra is a positive element) in $\mathfrak {L}(\mathcal {H})$, and if the left essential spectrum of $T$ is infinite, then $R{({\delta _T})^ - } + \{ {T^ \ast }\} ’$ is not norm dense in $\mathfrak {L}(\mathcal {H})$, where $R{({\delta _T})^ - }$ denotes the norm closure of the range of derivation induced by $T$, and $\{ {T^ \ast }\} ’$ denotes the commutant of ${T^ \ast }$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 44-48
  • MSC: Primary 47B20
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374974-7
  • MathSciNet review: 0374974