Polaroid operators and Weyl type theorems

Asian-European Journal of Mathematics ◽

10.1142/s1793557120501235 ◽

2019 ◽

Vol 13 (07) ◽

pp. 2050123

Author(s):

Salah Mecheri ◽

Naim L. Braha

Keyword(s):

Hilbert Space ◽

Analytic Function ◽

Complex Hilbert Space ◽

Basic Properties ◽

Polaroid Operators ◽

Weyl Type Theorems

Let [Formula: see text] be a [Formula: see text]-quasiposinormal operator on a complex Hilbert space [Formula: see text]. In this paper, we give basic properties for [Formula: see text] and we show that a [Formula: see text]-quasiposinormal operator [Formula: see text] is polaroid. We also prove that all Weyl type theorems (generalized or not) hold and are equivalent for [Formula: see text], where [Formula: see text] is an analytic function defined on a neighborhood of [Formula: see text].

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New extended Weyl type theorems and polaroid operators

Filomat ◽

10.2298/fil1306061j ◽

2013 ◽

Vol 27 (6) ◽

pp. 1061-1073

Author(s):

An Ju ◽

Min Han

Keyword(s):

Polaroid Operators ◽

Weyl Type Theorems

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Weyl Type Theorems for Left and Right Polaroid Operators

Integral Equations and Operator Theory ◽

10.1007/s00020-009-1738-2 ◽

2010 ◽

Vol 66 (1) ◽

pp. 1-20 ◽

Cited By ~ 34

Author(s):

Pietro Aiena ◽

Elvis Aponte ◽

Edixon Balzan

Keyword(s):

Polaroid Operators ◽

Weyl Type Theorems ◽

Left And Right

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WEYL TYPE THEOREMS FOR POSINORMAL OPERATORS

Mathematical Proceedings of the Royal Irish Academy ◽

10.3318/pria.2008.108.1.69 ◽

2008 ◽

Vol 108 (1) ◽

pp. 69-79

Author(s):

S. Mecheri ◽

Makhlouf Seddik

Keyword(s):

Weyl Type Theorems

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Local Spectral Properties Under Conjugations

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01731-7 ◽

2021 ◽

Vol 18 (3) ◽

Author(s):

Pietro Aiena ◽

Fabio Burderi ◽

Salvatore Triolo

Keyword(s):

Hilbert Space ◽

Spectral Properties ◽

Operator Matrices ◽

Weyl Type Theorems ◽

Triangular Operator ◽

Analytic Core ◽

Complex Symmetric ◽

Symmetric Operators ◽

The Relationship

AbstractIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.

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WEYL TYPE THEOREMS FOR FUNCTIONS OF OPERATORS

Glasgow Mathematical Journal ◽

10.1017/s0017089512000092 ◽

2012 ◽

Vol 54 (3) ◽

pp. 493-505 ◽

Cited By ~ 3

Author(s):

SEN ZHU ◽

CHUN GUANG LI ◽

TING TING ZHOU

Keyword(s):

Hilbert Spaces ◽

Linear Operators ◽

Weyl’S Theorem ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Compact Perturbations ◽

Weyl Type Theorems ◽

Necessary And Sufficient

AbstractA-Weyl's theorem and property (ω), as two variations of Weyl's theorem, were introduced by Rakočević. In this paper, we study a-Weyl's theorem and property (ω) for functions of bounded linear operators. A necessary and sufficient condition is given for an operator T to satisfy that f(T) obeys a-Weyl's theorem (property (ω)) for all f ∈ Hol(σ(T)). Also we investigate the small-compact perturbations of operators satisfying a-Weyl's theorem (property (ω)) in the setting of separable Hilbert spaces.

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A Unifying Approach to Weyl Type Theorems for Banach Space Operators

Integral Equations and Operator Theory ◽

10.1007/s00020-013-2097-6 ◽

2013 ◽

Vol 77 (3) ◽

pp. 371-384 ◽

Cited By ~ 10

Author(s):

Pietro Aiena ◽

Jesús R. Guillén ◽

Pedro Peña

Keyword(s):

Banach Space ◽

Weyl Type Theorems ◽

Banach Space Operators

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Propertiesandfor Bounded Linear Operators

Journal of Mathematics ◽

10.1155/2013/848176 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

M. H. M. Rashid

Keyword(s):

Type Theorem ◽

Main Tool ◽

Extension Property ◽

Complex Banach Space ◽

Linear Operators ◽

Weyl’S Theorem ◽

Bounded Linear Operators ◽

Single Valued Extension Property ◽

Bounded Linear ◽

Weyl Type Theorems

We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we callproperty, means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we callproperty, means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi--Fredholm with index less than or equal to 0. Properties and are related to a strong variants of classical Weyl’s theorem, the so-called property and property We shall characterize properties and in several ways and we shall also describe the relationships of it with the other variants of Weyl type theorems. Our main tool is localized version of the single valued extension property. Also, we consider the properties and in the frame of polaroid type operators.

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