scholarly journals STRICTLY SINGULAR PERTURBATION OF ALMOST SEMI-FREDHOLM LINEAR RELATIONS IN NORMED SPACES

2013 ◽  
Vol 56 (1) ◽  
pp. 211-219
Author(s):  
T. ÁLVAREZ
Keyword(s):  
Singular Perturbation ◽  
Linear Operators ◽  
Normed Spaces ◽  
Linear Relations ◽  
Perturbation Result ◽  
Strictly Singular ◽  
The Stability

AbstractIn this paper, we introduce the notions of almost upper semi-Fredholm and strictly singular pairs of subspaces and show that the class of almost upper semi-Fredholm pairs of subspaces is stable under strictly singular pairs perturbation. We apply this perturbation result to investigate the stability of almost semi-Fredholm multi-valued linear operators in normed spaces under strictly singular perturbation as well as the behaviour of the index under perturbation.

scholarly journals Quantities related to upper and lower semi-Fredholm type linear relations

2002 ◽  
Vol 66 (2) ◽  
pp. 275-289 ◽  
Author(s):  
Teresa Alvarez ◽  
Ronald Cross ◽  
Diane Wilcox
Keyword(s):  
Perturbation Theory ◽  
General Setting ◽  
Linear Operators ◽  
Normed Spaces ◽  
Fredholm Type ◽  
Linear Relations ◽  
Lower Semi ◽  
Strictly Singular

Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F− linear relations. Applications to perturbation theory follow.

scholarly journals Perturbation theory of multivalued atkinson operators in normed spaces

2007 ◽  
Vol 76 (2) ◽  
pp. 195-204 ◽  
Author(s):  
Teresa Álvarez ◽  
Diane Wilcox
Keyword(s):  
Perturbation Theory ◽  
Linear Operators ◽  
Normed Spaces ◽  
Linear Relations ◽  
Small Norm ◽  
Additive Perturbation ◽  
Strictly Singular ◽  
Stability Results

We prove several stability results for Atkinson linear relations under additive perturbation by small norm, strictly singular and strictly cosingular multivalued linear operators satisfying some additional conditions.

scholarly journals A KATO PERTURBATION-TYPE RESULT FOR OPEN LINEAR RELATIONS IN NORMED SPACES

2009 ◽  
Vol 79 (1) ◽  
pp. 85-101 ◽  
Author(s):  
DANA GHEORGHE
Keyword(s):  
Banach Space ◽  
Perturbation Theory ◽  
Topological Index ◽  
Sufficient Conditions ◽  
Type Result ◽  
Normed Spaces ◽  
Linear Relations ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Gap Topology

AbstractUsing some techniques of perturbation theory for Banach space complexes, we obtain necessary and sufficient conditions for the stability of the topological index of an open linear relation under small (with respect to the gap topology) perturbations with linear relations.

scholarly journals Linear relations on hereditarily indecomposable normed spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 289-300 ◽  
Author(s):  
Teresa Álvarez
Keyword(s):  
Normed Space ◽  
Linear Relation ◽  
Continuous Linear ◽  
Normed Spaces ◽  
Linear Relations ◽  
Dense Domain ◽  
Strictly Singular ◽  
Hereditarily Indecomposable

We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.

scholarly journals On the Stability of Self-Adjointness of Linear Relations

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Yan Liu
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Linear Relations ◽  
The Stability ◽  
Bounded Perturbations

This paper focuses on the stability of self-adjointness of linear relations under perturbations in Hilbert spaces. It is shown that a self-adjoint relation is still self-adjoint under bounded and relatively bounded perturbations. The results obtained in the present paper generalize the corresponding results for linear operators to linear relations, and some weaken the conditions of the related existing results.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

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