Operators in Rigged Hilbert spaces: some spectral properties

2013/09/16 by Bellomonte, G., Di Bella, S., Trapani, C.
#47L05 #47L60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1309.4038

Abstract

A notion of resolvent set for an operator acting in a rigged Hilbert space \D ⊂ \H⊂ \D^× is proposed. This set depends on a family of intermediate locally convex spaces living between \D and \D^×, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.

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