A characterization of the essential approximation pseudospectrum on a Banach space

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3599-3610 ◽  
Author(s):  
Aymen Ammar ◽  
Aref Jeribi ◽  
Kamel Mahfoudhi
Keyword(s):  
Banach Space ◽  
Approximation Theory ◽  
Linear Operators ◽  
The Stability ◽  
Densely Defined

One impetus for writing this paper is the issue of approximation pseudospectrum introduced by M. P. H.Wolff in the journal of approximation theory (2001). The latter study motivates us to investigate the essential approximation pseudospectrum of closed, densely defined linear operators on a Banach space. We begin by defining it and then we focus on the characterization, the stability and some properties of these pseudospectra.

scholarly journals Essential pseudospectra involving demicompact and pseudodemicompact operators and some perturbation results

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2519-2528 ◽  
Author(s):  
Fatma Brahim ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Fredholm Operators ◽  
The Stability ◽  
Stability Results ◽  
Densely Defined

In this paper, we study the essential and the structured essential pseudospectra of closed densely defined linear operators acting on a Banach space X. We start by giving a refinement and investigating the stability of these essential pseudospectra by means of the class of demicompact linear operators. Moreover, we introduce the notion of pseudo demicompactness and we study its relationship with pseudo upper semi-Fredholm operators. Some stability results for the Gustafson essential pseudospectrum involving pseudo demicompact operators is given.

scholarly journals The essential approximate pseudospectrum and related results

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2139-2151 ◽  
Author(s):  
Aymen Ammar ◽  
Aref Jeribi ◽  
Kamel Mahfoudhi
Keyword(s):  
Banach Space ◽  
Compact Operators ◽  
Linear Operators ◽  
The Stability ◽  
Densely Defined

In this paper, we introduce and study the essential approximate pseudospectrum of closed, densely defined linear operators in the Banach space. We begin by the definition and we investigate the characterization, the stability by means of quasi-compact operators and some properties of these pseudospectrum.

Characterization of Closed Densely Defined Semi-Browder Linear Operators

2012 ◽  
Vol 7 (6) ◽  
pp. 1775-1786 ◽  
Author(s):  
Teresa Alvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Linear Operators ◽  
Densely Defined

Stability of the S-essential spectra on a Banach space

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Faiçal Abdmouleh ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Essential Spectra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Projection

AbstractIn this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

scholarly journals Closed linear operators with domain containing their range

1984 ◽  
Vol 27 (2) ◽  
pp. 229-233 ◽  
Author(s):  
Schôichi Ôta
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Linear Operator ◽  
Linear Operators ◽  
Closed Linear Operator ◽  
Unbounded Operators ◽  
Densely Defined ◽  
Closed Linear Operators

In connection with algebras of unbounded operators, Lassner showed in [4] that, if T is a densely defined, closed linear operator in a Hilbert space such that its domain is contained in the domain of its adjoint T* and is globally invariant under T and T*,then T is bounded. In the case of a Banach space (in particular, a C*-algebra) weshowed in [6] that a densely defined closed derivation in a C*-algebra with domaincontaining its range is automatically bounded (see the references in [6] and [7] for thetheory of derivations in C*-algebras).

scholarly journals An algebraic characterization of complete inner product spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 47-53
Author(s):  
Vasile I. Istratescu
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Inner Product ◽  
Algebraic Characterization ◽  
Product Spaces ◽  
Bounded Linear Operators ◽  
Multiplicative Property ◽  
Bounded Linear ◽  
Inner Product Spaces

We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a “multiplicative” property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj.

scholarly journals Relatively compact-like perturbations, essential spectra and application

2004 ◽  
Vol 77 (1) ◽  
pp. 73-90 ◽  
Author(s):  
Khalid Latrach ◽  
J. Martin Paoli
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Neutron Transport ◽  
Linear Operators ◽  
Essential Spectra ◽  
Graph Norm ◽  
Bounded Linear ◽  
Neutron Transport Equations ◽  
Densely Defined ◽  
Fredholm Perturbations

AbstractThe purpose of this paper is to provide a detailed treatment of the behaviour of essential spectra of closed densely defined linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators. IfAdenotes a closed densely defined linear operator on a Banach spaceX, our approach consists principally in considering the class ofA-closable operators which, regarded as operators in ℒ(XA,X) (whereXAdenotes the domain ofAequipped with the graph norm), are contained in the set ofA-Fredholm perturbations (see Definition 1.2). Our results are used to describe the essential spectra of singular neutron transport equations in bounded geometries.

scholarly journals Generic stability of the spectra for bounded linear operators on Banach spaces

1999 ◽  
Vol 12 (1) ◽  
pp. 31-33
Author(s):  
Luo Qun
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Residual Subset ◽  
Bounded Linear ◽  
Generic Stability ◽  
The Stability

In this paper, we study the stability of the spectra of bounded linear operators B(X) in a Banach space X, and obtain that their spectra are stable on a dense residual subset of B(X).

Characterization of linear preservers of generalized majorization on c0

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4979-4988 ◽  
Author(s):  
Eshkaftaki Bayati ◽  
Noha Eftekhari
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Supremum Norm ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Linear Preservers

In this work we investigate a natural preorder on c0, the Banach space of all real sequences tend to zero with the supremum norm, which is said to be ?convex majorization?. Some interesting properties of all bounded linear operators T : c0 ? c0, preserving the convex majorization, are given and we characterize such operators.

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