Operators in Rigged Hilbert spaces: some spectral properties
Abstract
A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2013
- DOI:
- 10.48550/arXiv.1309.4038
- arXiv:
- arXiv:1309.4038
- Bibcode:
- 2013arXiv1309.4038B
- Keywords:
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- Mathematics - Functional Analysis;
- 47L60;
- 47L05
- E-Print:
- 29 pages