On the class of paranormal operators

Furuta, Takayuki

doi:10.3792/pja/1195521514

Cited by 86 publications

(50 citation statements)

References 7 publications

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“…Recall that powers of (closed) paranormal operators are (closed) paranormal [4][5][6]23]. It turns out that the same assertion remains true for 2-hyperexpansive operators (see § 4).…”

Section: Introductionmentioning

confidence: 90%

Unbounded 2-Hyperexpansive Operators

Jabłoński¹,

Stochel²

2001

Proceedings of the Edinburgh Mathematical Society

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It is shown that most properties of (bounded) completely hyperexpansive operators remain valid for unbounded 2-hyperexpansive operators. Powers of closed 2-hyperexpansive operators are proved to be closed and 2-hyperexpansive. Various parts of spectra of such operators are calculated. 2-hyperexpansive weighted shifts are investigated. Examples of unbounded closed 2-hyperexpansive (2-isometric) operators with invariant dense domains are established.

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“…Recall that powers of (closed) paranormal operators are (closed) paranormal [4][5][6]23]. It turns out that the same assertion remains true for 2-hyperexpansive operators (see § 4).…”

Section: Introductionmentioning

confidence: 90%

Unbounded 2-Hyperexpansive Operators

Jabłoński¹,

Stochel²

2001

Proceedings of the Edinburgh Mathematical Society

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“…Han [2] showed that Weyl's theorem holds for algebraically quasi-class A operators. Recall that [16,17]. In order to discuss the relations between paranormal and p-hyponormal and log-hyponormal operators (T is invertible and log T * T ≥ log T T * ), T. Furuta, M. Ito and T. Yamazaki [18] introduced a very interesting class of operators: class A defined by…”

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

confidence: 99%

Weyl's theorem for algebraically k-quasiclass A operators

Gao¹,

Fang²

2012

OpMath

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Abstract. If T or T * is an algebraically k-quasiclass A operator acting on an infinite dimensional separable Hilbert space and F is an operator commuting with T , and there exists a positive integer n such that F n has a finite rank, then we prove that Weyl's theorem holds for f (T ) + F for every f ∈ H(σ(T )), where H(σ(T )) denotes the set of all analytic functions in a neighborhood of σ(T ). Moreover, if T * is an algebraically k-quasiclass A operator, then α-Weyl's theorem holds for f (T ). Also, we prove that if T or T * is an algebraically k-quasiclass A operator then both the Weyl spectrum and the approximate point spectrum of T obey the spectral mapping theorem for every f ∈ H(σ(T )).

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“…, x n ) ∈ C n ; the inner product induced by this norm is denoted, as usual, by ·, · . Recall that an operator T ∈ B(H) is said to be paranormal (see [13,16]…”

Section: Towards L(n)-hyponormalitymentioning

confidence: 99%

L(n)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY

Jung¹,

Park²,

Stochel³

2010

J. Aust. Math. Soc.

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A new notion of L(n)-hyponormality is introduced in order to provide a bridge between subnormality and paranormality, two concepts which have received considerable attention from operator theorists since the 1950s. Criteria for L(n)-hyponormality are given. Relationships to other notions of hyponormality are discussed in the context of weighted shift and composition operators.2000 Mathematics subject classification: primary 47B20; secondary 47B33, 47B37.

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On the class of paranormal operators

Cited by 86 publications

References 7 publications

Unbounded 2-Hyperexpansive Operators

Unbounded 2-Hyperexpansive Operators

Weyl's theorem for algebraically k-quasiclass A operators

L(n)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY

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