On log-hyponormal operators

Tanahashi, Kôtarô

doi:10.1007/bf01300584

Cited by 88 publications

(34 citation statements)

References 13 publications

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“…The Löwner-Heinz inequality implies that if A is q-hyponormal then it is p-hyponormal for any 0 < p ≤ q. An invertible operator A is said to be loghyponormal ( [28]) if log(A * A) ≥ log(AA * ).…”

Section: S(x Rs (F )) = Y Sr (F ) ∩ S(x) and S(x Rs (F )) = Y Sr (F )mentioning

confidence: 99%

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Benhida

Zerouali²

2007

Perspectives in Operator Theory

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Section: S(x Rs (F )) = Y Sr (F ) ∩ S(x) and S(x Rs (F )) = Y Sr (F )mentioning

confidence: 99%

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Benhida

Zerouali²

2007

Perspectives in Operator Theory

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“…Log-hyponormal operators were introduced by Tanahashi [3], Aluthge and Wang [4], and Fujii et al [5] independently. Aluthge [6] introduced phyponormal operators.…”

Section: Introductionmentioning

confidence: 99%

Spectrum of Class wF(p,r,q) Operators

Yuan

Гао

2007

J. Inequal. Appl.

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Dedicated to Professor Daoxing Xia on his 77th birthday with respect and affectionRecommended by Jozsef Szabados This paper discusses some spectral properties of class wF(p,r, q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r, q) operator, then the Riesz idempotent E λ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and* . Afterwards, we prove that every class wF (p,r, q) operator has SVEP and property (β), and Weyl's theorem holds for f (T) when f ∈ H(σ(T)).

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“…It is known that invertible p-hyponormal operators are log-hyponormal but that the converse is not true [16]. However it is very interesting that we may regard log-hyponormal operators as 0-hyponormal operators [16,17].…”

Section: Introduction Let H and K Be Infinite Dimensional Complex Himentioning

confidence: 99%

“…However it is very interesting that we may regard log-hyponormal operators as 0-hyponormal operators [16,17]. Let T = U|T| be the polar decomposition of T. We usually define the Aluthge transform of T by T = |T| 1/2 U|T| 1/2 .…”

Section: Introduction Let H and K Be Infinite Dimensional Complex Himentioning

confidence: 99%

“…Let T = V | T| be the polar decomposition of T, and define the second Aluthge transform of T by T = | T| 1/2 V | T| 1/2 . It is known that if T is loghyponormal, then T is semi-hyponormal and T is hyponormal [1,16,21]. An operator X ∈ L(H 2 , H 1 ) is called a quasiaffinity if X is injective and has dense range R(X).…”

Section: Introduction Let H and K Be Infinite Dimensional Complex Himentioning

confidence: 99%

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