scholarly journals Generalized Kato decomposition, single-valued extension property and approximate point spectrum

2009 ◽  
Vol 356 (1) ◽  
pp. 322-327 ◽  
Author(s):  
Qiaofen Jiang ◽  
Huaijie Zhong
Keyword(s):  
Point Spectrum ◽  
Extension Property ◽  
Single Valued Extension Property ◽  
Approximate Point Spectrum ◽  
Generalized Kato Decomposition

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 Stability of essential approximate point spectrum and essential defect spectrum of linear operator

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 1983-1994
Author(s):  
Aymen Ammar ◽  
Mohammed Dhahri ◽  
Aref Jeribi
Keyword(s):  
Linear Operator ◽  
Measure Of Noncompactness ◽  
Point Spectrum ◽  
Fredholm Operators ◽  
Approximate Point Spectrum ◽  
Densely Defined

In the present paper, we use the notion of measure of noncompactness to give some results on Fredholm operators and we establish a fine description of the essential approximate point spectrum and the essential defect spectrum of a closed densely defined linear operator.

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 Subdivisions of the Spectra for the Operator D(r, 0, 0, s) over Certain Sequence Spaces

2016 ◽  
Vol 34 (1) ◽  
pp. 75-84 ◽  
Author(s):  
Avinoy Paul ◽  
Binod Chandra Tripathy
Keyword(s):  
Point Spectrum ◽  
Sequence Spaces ◽  
Approximate Point Spectrum

In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r, 0, 0, s)on the sequence spaces c0, c, ℓp and bvp.

scholarly journals Numerical Range of Two Operators in Semi-Inner Product Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
N. K. Sahu ◽  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Point Spectrum ◽  
Numerical Range ◽  
Linear Operators ◽  
Inner Product ◽  
Product Spaces ◽  
Inclusion Relation ◽  
Nonlinear Operators ◽  
Approximate Point Spectrum ◽  
Inner Product Spaces ◽  
Inclusion Relations

In this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operators. We also show the inclusion relation between approximate point spectrum and closure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.

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