scholarly journals On the Bonsall cone spectral radius and the approximate point spectrum

2017 ◽  
Vol 37 (10) ◽  
pp. 5337-5354 ◽  
Author(s):  
Vladimir Müller ◽  
◽  
Aljoša Peperko ◽  
◽  
Keyword(s):  
Spectral Radius ◽  
Point Spectrum ◽  
Approximate Point Spectrum

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 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.

scholarly journals Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space ()

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Karaisa ◽  
Feyzi Başar
Keyword(s):  
Continuous Spectrum ◽  
Sequence Space ◽  
Point Spectrum ◽  
Band Matrices ◽  
Residual Spectrum ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
The Matrix ◽  
Lower Triangular ◽  
Triple Band

The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space and we give some applications.

scholarly journals Joint spectra of operators on Banach space

1986 ◽  
Vol 28 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Muneo Chō
Keyword(s):  
Banach Space ◽  
Point Spectrum ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Joint Spectrum ◽  
Approximate Point Spectrum ◽  
Definition Of ◽  
Unit Vectors

Let X be a complex Banach space. We denote by B(X) the algebra of all bounded linear operators on X. Let = (T1, …, Tn) be a commuting n-tuple of operators on X. And let στ() and σ″() by Taylor's joint spectrum and the doubly commutant spectrum of , respectively. We refer the reader to Taylor [8] for the definition of στ() and σ″(), A point z = (z1,…, zn) of ℂn is in the joint approximate point spectrum σπ() of if there exists a sequence {xk} of unit vectors in X such that∥(Ti – zi)xk∥→0 as k → ∞ for i = 1, 2,…, n.

scholarly journals A Note on Property(gb)and Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Qingping Zeng ◽  
Huaijie Zhong
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Point Spectrum ◽  
Bounded Linear ◽  
Approximate Point Spectrum ◽  
Weyl Spectrum ◽  
Nilpotent Operators ◽  
The Stability ◽  
Quasinilpotent Operators ◽  
Study Property

An operatorT∈ℬ(X)defined on a Banach spaceXsatisfies property(gb)if the complement in the approximate point spectrumσa(T)of the upper semi-B-Weyl spectrumσSBF+-(T)coincides with the setΠ(T)of all poles of the resolvent ofT. In this paper, we continue to study property(gb)and the stability of it, for a bounded linear operatorTacting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, and by quasinilpotent operators commuting withT. Two counterexamples show that property(gb)in general is not preserved under commuting quasi-nilpotent perturbations or commuting finite rank perturbations.

scholarly journals Approximate point spectrum and commuting compact perturbations

1986 ◽  
Vol 28 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Vladimir Rakočević
Keyword(s):  
Banach Space ◽  
Essential Spectrum ◽  
Point Spectrum ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Complex Numbers ◽  
Approximate Point Spectrum ◽  
Infinite Dimensional ◽  
Compact Perturbations ◽  
Image Position

Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B (X) (K(X)). Let σ(A) and σa(A) denote, respectively, the spectrum and approximate point spectrum of an element A of B(X). Setσem(A)and σeb(A) are respectively Schechter's and Browder's essential spectrum of A ([16], [9]). σea (A) is a non-empty compact subset of the set of complex numbers ℂ and it is called the essential approximate point spectrum of A ([13], [14]). In this note we characterize σab(A) and show that if f is a function analytic in a neighborhood of σ(A), then σab(f(A)) = f(σab(A)). The relation between σa(A) and σeb(A), that is exhibited in this paper, resembles the relation between the σ(A) and the σeb(A), and it is reasonable to call σab(A) Browder's essential approximate point spectrum of A.

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