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April, 2005 Relations between principal functions of p-hyponormal operators
Muneo CHŌ, Tadasi HURUYA
J. Math. Soc. Japan 57(2): 605-618 (April, 2005). DOI: 10.2969/jmsj/1158242073

Abstract

Let T = U | T | be a bounded linear operator with the associated polar decomposition on a separable infinite dimensional Hilbert space. For 0 < t < 1 , let T t = | T | t U | T | 1 - t and g T and g T t be the principal functions of T and T t , respectively. We show that, if T is an invertible semi-hyponormal operator with trace class commutator [ | T | , U ] , then g T = g T t almost everywhere on C . As a biproduct we reprove Berger's theorem and index properties of invertible p -hyponormal operators.

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Muneo CHŌ. Tadasi HURUYA. "Relations between principal functions of p-hyponormal operators." J. Math. Soc. Japan 57 (2) 605 - 618, April, 2005. https://doi.org/10.2969/jmsj/1158242073

Information

Published: April, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1080.47020
MathSciNet: MR2123247
Digital Object Identifier: 10.2969/jmsj/1158242073

Subjects:
Primary: 47A10 , 47B20

Keywords: Hilbert space , principal function , Trace

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 2 • April, 2005
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