ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

doi:10.1016/S0252-9602(13)60073-9

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1187-1201.doi: 10.1016/S0252-9602(13)60073-9

ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

Souhir ELLEUCH|Maher MNIF

D´epartement de Math´ematiques, Universit´e de Sfax, Facult´e des Sciences de Sfax, Laboratoire de Physiques Math´ematiques, B.P. 1171, 3000 Sfax, Tunisie

收稿日期:2011-06-09 修回日期:2012-02-14 出版日期:2013-07-20 发布日期:2013-07-20

ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

Souhir ELLEUCH|Maher MNIF

D´epartement de Math´ematiques, Universit´e de Sfax, Facult´e des Sciences de Sfax, Laboratoire de Physiques Math´ematiques, B.P. 1171, 3000 Sfax, Tunisie

Received:2011-06-09 Revised:2012-02-14 Online:2013-07-20 Published:2013-07-20

摘要/Abstract

摘要：

When A ∈ LR(H) and B ∈ LR(K) are given, for C ∈ LR(K, H) we denote by M_C the linear relation acting on the infinite dimensional separable Hilbert space HKof the form M_C =

(A C ).

0 B
In this paper, we give the necessary and sufficient conditions on A and B for which M_C is upper semi-Fredholm with negative index or Weyl for some C ∈ LR(K, H).

关键词: linear relation, Fredholm and semi-Fredholm relation, essential approximate point spectra for linear relation

Abstract:

When A ∈ LR(H) and B ∈ LR(K) are given, for C ∈ LR(K, H) we denote by M_C the linear relation acting on the infinite dimensional separable Hilbert space HKof the form M_C =

(A C ).

0 B
In this paper, we give the necessary and sufficient conditions on A and B for which M_C is upper semi-Fredholm with negative index or Weyl for some C ∈ LR(K, H).

Key words: linear relation, Fredholm and semi-Fredholm relation, essential approximate point spectra for linear relation

中图分类号:

47A06

Souhir ELLEUCH, Maher MNIF. ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS[J]. 数学物理学报(英文版), 2013, 33(4): 1187-1201.

Souhir ELLEUCH, Maher MNIF. ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1187-1201.

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ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

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