scholarly journals On generalized Drazin-Riesz operators

2021 ◽  
Vol 39 (3) ◽  
pp. 115-122
Author(s):  
Abdelaziz Tajmouati ◽  
Mbarek Abkari
Keyword(s):  
Extension Property ◽  
Single Valued Extension Property ◽  
Riesz Operators

In this paper, we investigate the classes of operators as class of generalized Drazin Riesz operators. We give some results for these classes throught localized single valued extension property (SVEP). Some applications are given.

scholarly journals Biquasitriangularity and spectral continuity

1985 ◽  
Vol 26 (2) ◽  
pp. 177-180 ◽  
Author(s):  
Ridgley Lange
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Extension Property ◽  
Point Of View ◽  
Single Valued Extension Property ◽  
Continuity Theorem ◽  
Spectral Continuity ◽  
Necessary And Sufficient ◽  
Continuity Of The Spectrum

In [6] Conway and Morrell characterized those operators on Hilbert space that are points of continuity of the spectrum. They also gave necessary and sufficient conditions that a biquasitriangular operator be a point of spectral continuity. Our point of view in this note is slightly different. Given a point T of spectral continuity, we ask what can then be inferred. Several of our results deal with invariant subspaces. We also give some conditions characterizing a biquasitriangular point of spectral continuity (Theorem 3). One of these is that the operator and its adjoint both have the single-valued extension property.

Property (ω) and the Single-valued Extension Property

2021 ◽  
Vol 37 (8) ◽  
pp. 1254-1266
Author(s):  
Lei Dai ◽  
Xiao Hong Cao ◽  
Qi Guo
Keyword(s):  
Extension Property ◽  
Single Valued Extension Property

scholarly journals Property $(w)$ of upper triangular operator Matrices

2020 ◽  
Vol 51 (2) ◽  
pp. 81-99
Author(s):  
Mohammad M.H Rashid
Keyword(s):  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Extension Property ◽  
Operator Matrices ◽  
Single Valued Extension Property ◽  
Triangular Operator ◽  
Upper Triangular Operator Matrices ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Number Of Authors

Let $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}\in\LB(\x,\y)$ be be an upper triangulate Banach spaceoperator. The relationship between the spectra of $M_C$ and $M_0,$ and theirvarious distinguished parts, has been studied by a large number of authors inthe recent past. This paper brings forth the important role played by SVEP,the {\it single-valued extension property,} in the study of some of these relations. In this work, we prove necessary and sufficient conditions of implication of the type $M_0$ satisfies property $(w)$ $\Leftrightarrow$ $M_C$ satisfies property $(w)$ to hold. Moreover, we explore certain conditions on $T\in\LB(\hh)$ and $S\in\LB(\K)$ so that the direct sum $T\oplus S$ obeys property $(w)$, where $\hh$ and $\K$ are Hilbert spaces.

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.

scholarly journals Upper triangular operators with SVEP: Spectral properties

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 25-37 ◽  
Author(s):  
B.P. Duggal
Keyword(s):  
Banach Space ◽  
Spectral Properties ◽  
Extension Property ◽  
Complex Banach Space ◽  
Single Valued Extension Property ◽  
Infinite Dimensional

Spectral properties of upper triangular operators T = (Tij)1?i,j?n E B(?n) where ?n = ?ni=1?i and ?i is an infinite dimensional complex Banach space such that Tii - ? has the single-valued extension property, SVEP, for all complex ? are studied.

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