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Hyponormal Operators with Infinite Essential Spectrum

Hong W. Kim
Proceedings of the American Mathematical Society
Vol. 51, No. 1 (Aug., 1975), pp. 44-48
DOI: 10.2307/2039843
Stable URL: http://www.jstor.org/stable/2039843
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hyponormal Operators with Infinite Essential Spectrum
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Abstract

It is shown that if T is an essentially hyponormal operator (i.e., the image of T* T - TT* in the Calkin algebra is a positive element) in L(H), and if the left essential spectrum of T is infinite, then R(δT)- + {T*}' is not norm dense in L(H), where R(δT)- denotes the norm closure of the range of derivation induced by T, and {T*}' denotes the commutant of T*.

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