6533b7dcfe1ef96bd1271d91
RESEARCH PRODUCT
Some spectral properties for operators acting on Rigged Hilbert spaces
Salvatore Di Bellasubject
PhysicsPure mathematicssymbols.namesakeSpectral theoryResolvent setLocally convex topological vector spaceHilbert spacesymbolsRigged Hilbert spaceOperator theoryCompact operator on Hilbert spaceResolventdescription
Operators on Rigged Hilbert spaces have been considered from the 80s of the 20th century on as good ones for describing several physical models whose observable set didn’t turn out to be a C∗-algebra.A notion of resolvent set for an operator acting in a rigged Hilbert space \(\mathcal{D}\subset \mathcal{H}\subset \mathcal{D}^{\times }\) is proposed. This set depends on a family of intermediate locally convex spaces living between \(\mathcal{D}\) and \(\mathcal{D}^{\times }\), called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 |