Communications of the
Korean Mathematical Society CKMS

In this paper, we denote by $\mathcal{L}$ the block matrix linear relation, acting on the Banach space $X\oplus Y$, of the form $$\mathcal{L}= \left( \begin{array}{cc} A & B\\ C & D \\ \end{array} \right),$$ 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 \ref{411114111111} and \ref{4111141111110}). Second we study Shechter spectra using demicompact linear relations and relatively demicompact linear relations (see Theorem \ref{120120120}).

Keywords: Linear relations, relatively demicompact linear relation, demicompact block matrix linear relation

MSC numbers: Primary 47A06