Trace formulae for p-hyponormal operators

Chō, Muneo; Huruya, Tadasi

doi:10.4064/sm161-1-1

Cited by 11 publications

(6 citation statements)

References 2 publications

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“…For example, if T is either normal or hyponormal, then T satisfies (1) (2). More generally, (1) (2) hold if T is semi-hyponormal [4], p-hyponormal [5] or log-hyponormal [6], [7,Corollary 4.5]. In [8], Duggal introduced a class K(p) of operators which contains the p-hyponormal operators and showed [8,Theorem 4] that operators T in the class K(p) satisfy (1), (2).…”

Section: An Operator T ∈ B(h) Is Called Weyl If It Is Fredholm Of Indmentioning

confidence: 99%

Spectrum of class absolute -*-k-paranormal operators for 0 ≤ k ≤ 1

Yang

Jun-li

2013

Filomat

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In this paper, we shall introduce a new class absolute-*-k-paranormal operators given by a norm inequality and *-A(k) operator by operator inequality, we will discuss the inclusion relation of them. And we study spectral properties of class absolute-*-k-paranormal operators. We show that if T belongs to class absolute-*-k-paranormal operators, then its point spectrum and joint point spectrum are identical, its approximate point spectrum and joint approximate point spectrum are identical. Next as an application of them, for Weyl spectrum w(•) and essential approximate point spectrum σ ea (•), we will show that if T or T * is absolute-*-k-paranormal for 0 ≤ k ≤ 1, then w(f (T)) = f (w(T)), σ ea (f (T)) = f (σ ea (T)) for every f ∈ H(σ(T)) where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T).

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Section: An Operator T ∈ B(h) Is Called Weyl If It Is Fredholm Of Indmentioning

confidence: 99%

Spectrum of class absolute -*-k-paranormal operators for 0 ≤ k ≤ 1

Yang

Jun-li

2013

Filomat

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“…H) for each λ ∈ C and hence T satisfies condition (N). Moreover, every p-hyponormal operator satisfies condition (N) ( [6]) and every log-hyponormal operator satisfies condition (N) ( [22]). and…”

Section: Here ∂σ(T ) Means the Boundary Of σ(T )mentioning

confidence: 99%

Analysis of Non-normal Operators via Aluthge Transformation

Kimura

2004

Integr. equ. oper. theory

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Let T be a bounded linear operator on a complex Hilbert space H. In this paper, we show that T has Bishop's property (β) if and only if its Aluthge transformationT has property (β). As applications, we can obtain the following results. Every w-hyponormal operator has property (β). Quasi-similar w-hyponormal operators have equal spectra and equal essential spectra. Moreover, in the last section, we consider Chō's problem that whether the semi-hyponormality of T implies the spectral mapping theorem Re σ(T ) = σ(Re T ) or not. (2000). Primary 47B20; Secondary 47A10, 47B40. Mathematics Subject Classification

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“…Let T 12 = V 12 | T 12 |, and define T 12 = | T 12 | 1/2 V 12 | T 12 | 1/2 . Letting W = | T 12 | 1/2 |T 12 | 1/2 , by the kernel condition proved in [3,Theorem 4] we can see that W is a quasiaffinity such that T 12 W = W T 12 . Now, let T 1 = T 11 ⊕ T 12 and Y = I H 11 ⊕ W .…”

Section: P-hyponormal Operators and Quasisimilarity 399mentioning

confidence: 99%

“…Recall( [1], [3], [4], [8], [12], [13], [16]) that an operator T ∈ L(H) is called p-hyponormal if (T * T ) p − (T T * ) p ≥ 0 for some 0 < p ≤ 1. If p = 1, T is said to be hyponormal and if p = 1/2, T is said to be semi-hyponormal ( [19]).…”

Section: Introductionmentioning

confidence: 99%