On $p$-hyponormal contractions
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- by B. P. Duggal PDF
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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.References
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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