Characterizations of closed decomposable operators (Q1066069)

In this paper, the authors endow a given closed operator with a weaker constituent than that of the spectral resolvent and obtain a new criterion for its spectral decomposition (Corollary 2.3). In Section 3, they introduce a concept weaker than that of spectral capacity for a closed operator and again obtain a simpler description of its spectral decomposition (Theorem 3.3). Finally, they extend a property of a bounded decomposable operator to the unbounded case (Corollary 3.5) and find conditions for a specific linear manifold, occurring in the theory of spectral capacities, to be dense in the underlying space (Theorem 3.6).