Acta mathematica scientia, Series B >
ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS
Received date: 2011-06-09
Revised date: 2012-02-14
Online published: 2013-07-20
When A ∈ 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).
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 . DOI: 10.1016/S0252-9602(13)60073-9
[1] Cross R W. Multivalued Linear Operators. New York: Dekker, 1998
[2] Cross R W. An index theorem for the product of linear relations. Linear Alg Appl, 1998, 277: 127–134
[3] Azizov T Y, Behrndt J, Jonas P, Trunk C. Compact and finite rank perturbations of linear relations in Hilbert spaces. Integral Equations Operator Theory, 2009, 63: 151–163
[4] Cao X H, Meng B. Essential approximate point spectra and Weyl´s theorem for operator matrices. J Math Anal Appl, 2005, 304: 759–771
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