scholarly journals Dynamical systems method for solving linear finite-rank operator equations

2009 ◽  
Vol 95 (1) ◽  
pp. 77-93 ◽  
Author(s):  
N. S. Hoang ◽  
A. G. Ramm
Keyword(s):  
Dynamical Systems ◽  
Finite Rank ◽  
Operator Equations ◽  
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 Aperiodic substitution systems and their Bratteli diagrams

2009 ◽  
Vol 29 (1) ◽  
pp. 37-72 ◽  
Author(s):  
S. BEZUGLYI ◽  
J. KWIATKOWSKI ◽  
K. MEDYNETS
Keyword(s):  
Dynamical Systems ◽  
Finite Rank ◽  
Bratteli Diagram ◽  
Bratteli Diagrams ◽  
Substitution Dynamical Systems ◽  
Substitution System ◽  
Minimal Component

AbstractWe study aperiodic substitution dynamical systems arising from non-primitive substitutions. We prove that the Vershik homeomorphism φ of a stationary ordered Bratteli diagram is topologically conjugate to an aperiodic substitution system if and only if no restriction of φ to a minimal component is conjugate to an odometer. We also show that every aperiodic substitution system generated by a substitution with nesting property is conjugate to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitution system is recognizable. The classes of m-primitive substitutions and derivative substitutions associated with them are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.

scholarly journals Perfect Orderings on Finite Rank Bratteli Diagrams

2014 ◽  
Vol 66 (1) ◽  
pp. 57-101 ◽  
Author(s):  
S. Bezuglyi ◽  
J. Kwiatkowski ◽  
R. Yassawi
Keyword(s):  
Dynamical Systems ◽  
Finite Rank ◽  
Sufficient Conditions ◽  
The Other ◽  
Bratteli Diagram ◽  
Incidence Matrices ◽  
Bratteli Diagrams ◽  
Topological Dynamical Systems ◽  
Almost All ◽  
Necessary And Sufficient

AbstractGiven a Bratteli diagram B, we study the set 𝒪B of all possible orderings on B and its subset PB consisting of perfect orderings that produce Bratteli–Vershik topological dynamical systems (Vershik maps). We give necessary and sufficient conditions for the ordering ω to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths constrains significantly the values of the entries of the incidence matrices and the structure of the diagram B. Our proofs are based on the new notions of skeletons and associated graphs, defined and studied in the paper. For a Bratteli diagram B of rank k, we endow the set 𝒪B with product measure μ and prove that there is some 1 ≤ j ≤ k such that μ-almost all orderings on B have j maximal and j minimal paths. If j is strictly greater than the number of minimal components that B has, then μ-almost all orderings are imperfect.

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