SHECHTER SPECTRA AND RELATIVELY DEMICOMPACT LINEAR RELATIONS

In this paper, we denote by L the block matrix linear relation, acting on the Banach space X ⊕ Y, of the form ${\mathcal{L}}=\(\array{A&B\\C&D}\)$, where A, B, C and D are four linear relations with dense domains. We first try to determine the conditions under which a block matrix linear relation becomes a demicompact block matrix linear relation (see Theorems 4.1 and 4.2). Second we study Shechter spectra using demicompact linear relations and relatively demicompact linear relations (see Theorem 5.1).