Spectra and measure inequalities
Author:
C. R. Putnam
Journal:
Trans. Amer. Math. Soc. 231 (1977), 519529
MSC:
Primary 47A30
MathSciNet review:
0487511
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Abstract: Let T be a bounded operator on a Hilbert space and let . Then the operators , and are nonnegative for all complex numbers z, t, and s. We shall obtain some norm estimates for nonnegative lower bounds of these operators, when z, t, and s are restricted to certain sets, in terms of certain capacities or area measures involving the spectrum and point spectrum of T. A typical such estimate is the following special case of Theorem 4 below: Let be separable and suppose that for all z and t not belonging to the closure of the interior of the point spectrum of T. In addition, suppose that the boundary of the interior of the point spectrum of T has Lebesgue planar measure 0. Then . If T is the adjoint of the simple unilateral shift, then equality holds with .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719770487511X
PII:
S 00029947(1977)0487511X
Keywords:
Hilbert space,
spectra of operators,
hyponormal operators,
analytic capacity,
continuous analytic capacity,
planar measure
Article copyright:
© Copyright 1977
American Mathematical Society
