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 on a Hilbert space is said to be completely hyponormal if and if has no nontrivial reducing space on which it is normal. If 0 is in the spectrum of such an operator and if the spectrum of near 0 is not ``too dense,'' then the unbounded operator acts as though it were bounded. In particular, under certain conditions, has a rectangular representation with absolutely continuous real and imaginary parts whose spectra are the closures of the projections of the spectrum of onto the coordinate axes.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291848-8

Keywords:
Hyponormal operators,
absolutely continuous operators

Article copyright:
© Copyright 1972
American Mathematical Society