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 The spectrum of an R-homomorphism

1977 ◽  
Vol 23 (1) ◽  
pp. 42-45 ◽  
Author(s):  
A. W. Wickstead
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Real Banach Space ◽  
Point Spectrum ◽  
Positive Linear Operator ◽  
Riesz Decomposition Property ◽  
Decomposition Property ◽  
Approximate Point Spectrum ◽  
Riesz Decomposition ◽  
The Riesz Decomposition Property

AbstractLet E be a real Banach space ordered by a closed, normal and generating cone. Suppose also that the order induced on E has the Riesz decomposition property. It is shown that if T:E → E is a positive linear operator with the property that y, z, a ∈ E with a ≧ Ty, Tz implies there is x ∈ E with x ≧ y, z and a ≧ Tx then the approximate point spectrum and spectrum of T are cyclic subsets of the complex plane. That is, if α = |α|γ lies in one of these sets then so does |α|γk for all integers k.

scholarly journals Spectral theory for polynomially demicompact operators

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2017-2030
Author(s):  
Fatma Brahim ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Linear Operator ◽  
Spectral Theory ◽  
Fredholm Operators ◽  
Essential Spectra ◽  
Densely Defined

In this article, we introduce the notion of polynomial demicompactness and we use it to give some results on Fredholm operators and to establish a fine description of some essential spectra of a closed densely defined linear operator. Our work is a generalization of many known ones in the literature.

Formally Normal Operators Having no Normal Extensions

1965 ◽  
Vol 17 ◽  
pp. 1030-1040 ◽  
Author(s):  
Earl A. Coddington
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Null Space ◽  
Normal Operator ◽  
Closed Linear Operator ◽  
Normal Operators ◽  
The Given ◽  
Densely Defined ◽  
Made In

The domain and null space of an operator A in a Hilbert space will be denoted by and , respectively. A formally normal operatorN in is a densely defined closed (linear) operator such that , and for all A normal operator in is a formally normal operator N satisfying 35 . A study of the possibility of extending a formally normal operator N to a normal operator in the given , or in a larger Hilbert space, was made in (1).

scholarly journals Dirac structures on Hilbert spaces

1999 ◽  
Vol 22 (1) ◽  
pp. 97-108 ◽  
Author(s):  
A. Parsian ◽  
A. Shafei Deh Abad
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Hilbert Spaces ◽  
Smooth Manifold ◽  
Real Hilbert Space ◽  
Dirac Structure ◽  
Dirac Structures ◽  
Basic Properties ◽  
Hilbert Subspace ◽  
Densely Defined

For a real Hilbert space(H,〈,〉), a subspaceL⊂H⊕His said to be a Dirac structure onHif it is maximally isotropic with respect to the pairing〈(x,y),(x′,y′)〉+=(1/2)(〈x,y′〉+〈x′,y〉). By investigating some basic properties of these structures, it is shown that Dirac structures onHare in one-to-one correspondence with isometries onH, and, any two Dirac structures are isometric. It is, also, proved that any Dirac structure on a smooth manifold in the sense of [1] yields a Dirac structure on some Hilbert space. The graph of any densely defined skew symmetric linear operator on a Hilbert space is, also, shown to be a Dirac structure. For a Dirac structureLonH, everyz∈His uniquely decomposed asz=p1(l)+p2(l)for somel∈L, wherep1andp2are projections. Whenp1(L)is closed, for any Hilbert subspaceW⊂H, an induced Dirac structure onWis introduced. The latter concept has also been generalized.

scholarly journals Measure of noncompactness of operators and matrices on the spacescandc0

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Bruno De Malafosse ◽  
Eberhard Malkowsky ◽  
Vladimir Rakocevic
Keyword(s):  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Necessary And Sufficient

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spacescandc0to be compact. Among other things, some results of Cohen and Dunford are recovered.

scholarly journals Derivations, local derivations and atomic boolean subspace lattices

2002 ◽  
Vol 66 (3) ◽  
pp. 477-486 ◽  
Author(s):  
Pengtong Li ◽  
Jipu Ma
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Linear Operator ◽  
Subspace Lattice ◽  
Local Derivation ◽  
Densely Defined ◽  
Subspace Lattices

Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.

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.

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