Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (4): 1187-1201.doi: 10.1016/S0252-9602(13)60073-9

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ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

Souhir ELLEUCH|Maher MNIF   

  1. 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

Abstract:

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

(A  C ).                                                                                                            

0   B
In this paper, we give the necessary and sufficient conditions on A and B for which MC 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

CLC Number: 

  • 47A06
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