Isolated spectral points of a linear relation

On isolated points of the approximate point spectrum of a closed linear relation

“…The main objective of this section is to give necessary conditions to ensure that the approximate point spectrum of a closed linear relation T does not cluster at a point λ. To do this, we begin with a generalization to the case of closed linear relations of a theorem stated in [9] dealing with the characterization of isolated points of the spectrum of a bounded closed linear relation. For this, we need the following technical lemma.…”

“…In recent years, the study of isolated spectral points of a multivalued linear operator (linear relation) has generated a great deal of research attention. It was proved in [9] that for a closed and bounded linear relation T such that 0 is a point of its spectrum, we have the equivalence: 0 is isolated in the spectrum of T ⇐⇒ H 0 (T ) and K(T ) are closed and X = H 0 (T ) ⊕ K(T ).…”