Polaroid operators and Weyl type theorems

2015 ◽  
pp. 1-20
Author(s):  
Pietro Aiena
Keyword(s):  
Polaroid Operators ◽  
Weyl Type Theorems

Polaroid operators and Weyl type theorems

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].

scholarly journals New extended Weyl type theorems and polaroid operators

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 1061-1073
Author(s):  
An Ju ◽  
Min Han
Keyword(s):  
Polaroid Operators ◽  
Weyl Type Theorems

Weyl Type Theorems for Left and Right Polaroid Operators

2010 ◽  
Vol 66 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Pietro Aiena ◽  
Elvis Aponte ◽  
Edixon Balzan
Keyword(s):  
Polaroid Operators ◽  
Weyl Type Theorems ◽  
Left And Right

WEYL TYPE THEOREMS FOR POSINORMAL OPERATORS

2008 ◽  
Vol 108 (1) ◽  
pp. 69-79
Author(s):  
S. Mecheri ◽  
Makhlouf Seddik
Keyword(s):  
Weyl Type Theorems

scholarly journals Local Spectral Properties Under Conjugations

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.

scholarly journals WEYL TYPE THEOREMS FOR FUNCTIONS OF OPERATORS

2012 ◽  
Vol 54 (3) ◽  
pp. 493-505 ◽  
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.

scholarly journals A Unifying Approach to Weyl Type Theorems for Banach Space Operators

2013 ◽  
Vol 77 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Pietro Aiena ◽  
Jesús R. Guillén ◽  
Pedro Peña
Keyword(s):  
Banach Space ◽  
Weyl Type Theorems ◽  
Banach Space Operators

scholarly journals Propertiesandfor Bounded Linear Operators

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.

A note on Weyl-type theorems and restrictions

2017 ◽  
Vol 8 (2) ◽  
pp. 190-198 ◽  
Author(s):  
Lihong Chen ◽  
Weigang Su
Keyword(s):  
Weyl Type Theorems

scholarly journals Weyl type theorems for Cesàro-hypercyclic operators

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5639-5644
Author(s):  
Abdelaziz Tajmouati ◽  
Berrag El
Keyword(s):  
Type Theorem ◽  
Hypercyclic Operators ◽  
Weyl Type Theorems

In this paper we study the relations between Ces?ro-hypercyclic operators and the operators for which Weyl type theorem holds.

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