An approximation problem of the finite rank operator in Banach spaces

2003 ◽  
Vol 46 (2) ◽  
pp. 245 ◽  
Author(s):  
Yuwen WANG
Keyword(s):  
Banach Spaces ◽  
Finite Rank ◽  
Approximation Problem ◽  
Finite Rank Operator ◽  
Rank Operator

Left-right fredholm and left-right browder linear relations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 255-271 ◽  
Author(s):  
T. Álvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Linear Relation ◽  
Finite Rank Operator ◽  
Linear Relations ◽  
Rank Operator ◽  
Type Decomposition ◽  
Converse Results

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.

scholarly journals On the stability of the spectral properties under commuting perturbations

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1511-1518
Author(s):  
Kai Yan ◽  
Weigang Su ◽  
Xiaochun Fang
Keyword(s):  
Finite Rank ◽  
Spectral Properties ◽  
Finite Rank Operator ◽  
Rank Operator ◽  
Algebraic Operator ◽  
The Stability

In this paper, we examine the stability of several spectral properties under commuting perturbations. In particular, we show that if T ( L(X) is an isoloid operator satisfying generalized Weyl?s theorem and if F ( L(X) is a power finite rank operator that commutes with T, then generalized Weyl?s theorem holds for T + F. In addition, we consider the permanence of Bishop?s property (?), at a point, under commuting perturbation that is an algebraic operator.

scholarly journals Decomposability of finite rank operators in certain subspaces and algebras

2001 ◽  
Vol 64 (2) ◽  
pp. 307-314
Author(s):  
Jiankui Li
Keyword(s):  
Hilbert Space ◽  
Finite Rank ◽  
Bounded Operators ◽  
Subspace Lattice ◽  
Finite Rank Operator ◽  
Rank Operator ◽  
Finite Rank Operators ◽  
Reflexive Algebra ◽  
Reflexive Subspace ◽  
Rank One

Let  be either a reflexive subspace or a bimodule of a reflexive algebra in B (H), the set of bounded operators on a Hilbert space H. We find some conditions such that a finite rank T ∈  has a rank one summand in  and  has strong decomposability. Let (ℒ) be the set of all operators on H that annihilate all the operators of rank at most one in alg ℒ. We construct an atomic Boolean subspace lattice ℒ on H such that there is a finite rank operator T in (ℒ) such that T does not have a rank one summand in (ℒ). We obtain some lattice-theoretic conditions on a subspace lattice ℒ which imply alg ℒ is strongly decomposable.

scholarly journals FINITE RANK RIESZ OPERATORS

2013 ◽  
Vol 56 (1) ◽  
pp. 183-185 ◽  
Author(s):  
U. KOUMBA ◽  
H. RAUBENHEIMER
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Riesz Operator ◽  
Finite Rank Operator ◽  
Rank Operator ◽  
Riesz Operators

AbstractWe provide conditions under which a Riesz operator defined on a Banach space is a finite rank operator.

scholarly journals Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank

2004 ◽  
Vol 330 (1) ◽  
Author(s):  
Julio Becerra Guerrero ◽  
Gin�s L�pez P�rez ◽  
Antonio M. Peralta ◽  
A Rodr�guez-Palacios
Keyword(s):  
Banach Spaces ◽  
Finite Rank

scholarly journals Strong Convergence Theorems for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Nonself Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Liang-cai Zhao ◽  
Shih-sen Chang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Approximation Problem ◽  
Countable Family ◽  
Convergence Theorems ◽  
Limit Condition ◽  
Asymptotically Nonexpansive ◽  
System Of Equilibrium Problems

The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

Semi-Fredholm perturbations and commutators

1993 ◽  
Vol 113 (1) ◽  
pp. 173-177 ◽  
Author(s):  
Mostafa Mbekhta
Keyword(s):  
Banach Spaces ◽  
Finite Rank ◽  
Fredholm Operators ◽  
Densely Defined ◽  
Fredholm Perturbations

AbstractThe Laffey–West theorem concerning finite rank perturbations of bounded Fredholm operators is extended to closed densely defined operators on Banach Spaces.

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