Spectra for upper triangular linear relation matrices through local spectral theory

Let X and Y be Banach spaces. When A and B are linear relations in X and Y, respectively, we denote by MC the linear relation in X x Y of the form ((A C) (0 B)), where 0 is the zero operator from X to Y and C is a bounded operator from Y to X. In this paper, by using properties of the SVEP, we study the defect set (Sigma(A) boolean OR Sigma(B))\Sigma(M-C), where Sigma is the spectrum, the approximate point spectrum, the surjective spectrum, the Fredholm spectrum, the Weyl spectrum, the Browder spectrum, the generalized Drazin spectrum and the Drazin spectrum.