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Proceedings of the American Mathematical Society

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



The spectra of unbounded hyponormal operators

Author: C. R. Putnam
Journal: Proc. Amer. Math. Soc. 31 (1972), 458-464
MSC: Primary 47B20
MathSciNet review: 0291848
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Abstract: A bounded operator $ T$ on a Hilbert space is said to be completely hyponormal if $ {T^\ast}T - T{T^\ast} \geqq 0$ and if $ T$ has no nontrivial reducing space on which it is normal. If 0 is in the spectrum of such an operator $ T$ and if the spectrum of $ T$ near 0 is not ``too dense,'' then the unbounded operator $ {T^{ - 1}}$ acts as though it were bounded. In particular, under certain conditions, $ {T^{ - 1}}$ has a rectangular representation with absolutely continuous real and imaginary parts whose spectra are the closures of the projections of the spectrum of $ {T^{ - 1}}$ onto the coordinate axes.

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Keywords: Hyponormal operators, absolutely continuous operators
Article copyright: © Copyright 1972 American Mathematical Society

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