Essential Approximate Point Spectra for Upper Triangular Matrix of Linear Relations

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