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.

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 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 On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6337-6355 ◽  
Author(s):  
Bouaniza Hafsa ◽  
Maher Mnif
Keyword(s):  
Finite Rank ◽  
Linear Relation ◽  
Linear Relations ◽  
Finite Rank Operators ◽  
Lower Semi ◽  
The Stability

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.

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 Structure and spectal properties of cinnamoyl pyrones and their vinylogs

2010 ◽  
Vol 8 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Dmytro Tykhanov ◽  
Irina Serikova ◽  
Fedor Yaremenko ◽  
Alexander Roshal
Keyword(s):  
Quantum Chemical ◽  
Spectral Properties ◽  
Solvent Polarity ◽  
Polymethine Chain ◽  
Quantum Chemical Analysis ◽  
Polar Solvents ◽  
Trans Conformation ◽  
The Stability ◽  
The Relationship ◽  
Cinnamoyl Pyrones

AbstractThe 1H-NMR and quantum chemical analysis of the stability of tautomers of cinnamoyl pyrone derivatives and vinylogs has been studied. The relationship between the structure of the most stable tautomer and its spectral properties has been investigated. It has been determined that the tautomer of highest stability (88–100 molar %) has an α-pyrone structure and exhibits a trans-conformation in the cinnamoyl fragment. An intense fluorescence of dyes has been observed in non-polar solvents with cinnamoyl fragments having electron-donating substituents or several double bonds in the polymethine chain. A gradient in solvent polarity resulted in fluorescence quenching which permits the use of the dyes as intensometric fluorometric probes for medium polarity examination.

scholarly journals Review on the Stability of the Peregrine and Related Breathers

2020 ◽  
Vol 8 ◽  
Author(s):  
Miguel A. Alejo ◽  
Luca Fanelli ◽  
Claudio Muñoz
Keyword(s):  
Spectral Properties ◽  
Lyapunov Functionals ◽  
Nonlinear Odes ◽  
First Variation ◽  
Standard Definition ◽  
Nonlinear Schrödinger ◽  
Open Questions ◽  
The First Variation ◽  
The Stability ◽  
Definition Of

In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned.

On the Stability of Singular Finite-Rank Methods

1990 ◽  
Vol 27 (3) ◽  
pp. 792-803 ◽  
Author(s):  
Lalita N. Deshpande ◽  
Balmohan V. Limaye
Keyword(s):  
Finite Rank ◽  
The Stability
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