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