Additive Mappings Preserving Fredholm Operators with Fixed Nullity or Defect

2021 ◽  
Vol 41 (5) ◽  
pp. 1670-1678
Author(s):  
Ruihan Zhang ◽  
Weijuan Shi ◽  
Guoxing Ji
Keyword(s):  
Fredholm Operators ◽  
Additive Mappings

On Traces of n-Additive Mappings on Semiprime Ring

2017 ◽  
Vol 4 (1) ◽  
pp. 1-10
Author(s):  
Najat Muthana ◽  
◽  
Asma Ali ◽  
Kapil Kumar
Keyword(s):  
Semiprime Ring ◽  
Additive Mappings

Global Perturbation of Nonlinear Eigenvalues

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián López-Gómez ◽  
Juan Carlos Sampedro
Keyword(s):  
Perturbation Theory ◽  
Spectral Parameter ◽  
Classical Theory ◽  
General Setting ◽  
Perturbation Parameter ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Index Zero ◽  
Finite Dimensional ◽  
Nonlinear Eigenvalues

Abstract This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ⁢ ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ⁢ ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ⁢ ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

Economical finite rank perturbations of semi-Fredholm operators

1988 ◽  
Vol 198 (3) ◽  
pp. 431-434 ◽  
Author(s):  
M�che�l � Searc�id
Keyword(s):  
Finite Rank ◽  
Fredholm Operators

scholarly journals Additive mappings that preserve rank one nilpotent operators

2003 ◽  
Vol 367 ◽  
pp. 213-224 ◽  
Author(s):  
Wu Jing ◽  
Pengtong Li ◽  
Shijie Lu
Keyword(s):  
Nilpotent Operators ◽  
Rank One ◽  
Additive Mappings

scholarly journals On stability of additive mappings

1991 ◽  
Vol 14 (3) ◽  
pp. 431-434 ◽  
Author(s):  
Zbigniew Gajda
Keyword(s):  
Additive Mappings

In this paper we answer a question of Th. M. Rassias concerning an extension of validity of his result proved in [3].

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