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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On $p$-hyponormal contractions
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by B. P. Duggal PDF
Proc. Amer. Math. Soc. 123 (1995), 81-86 Request permission

Abstract:

The contraction A on a Hilbert space H is said to be p-hyponormal, $0 < p < 1$, if ${({A^ \ast }A)^p} \geq {(A{A^ \ast })^p}$. Let A be an invertible p-hyponormal contraction. It is shown that A has ${C_{.0}}$ completely nonunitary part. Now let H be separable. If A is pure and the defect operator ${D_A} = {(1 - {A^ \ast }A)^{1/2}}$ is of Hilbert-Schmidt class, then $A \in {C_{10}}$. Let ${B^ \ast }$ be a contraction such that ${B^\ast }$ has ${C_{.0}}$ completely nonunitary part, ${D_{{B^ \ast }}}$ is of Hilbert-Schmidt class, and ${B^ \ast }$ satisfies the property that if the restriction of ${B^ \ast }$ to an invariant subspace is normal, then the subspace reduces ${B^ \ast }$. It is shown that if $AX = XB$ for some quasi-affinity X, then A and B are unitarily equivalent normal contractions.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 81-86
  • MSC: Primary 47B20; Secondary 47A10, 47B10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1264808-3
  • MathSciNet review: 1264808