Rigged Hilbert spaces and contractive families of Hilbert spaces |
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Authors: | Giorgia Bellomonte Camillo Trapani |
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Institution: | 1. Dipartimento di Matematica e Informatica, Universit?? di Palermo, Via Archirafi 34, 90123, Palermo, Italy
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Abstract: | The existence of a rigged Hilbert space whose extreme spaces are, respectively, the projective and the inductive limit of a directed contractive family of Hilbert spaces is investigated. It is proved that, when it exists, this rigged Hilbert space is the same as the canonical rigged Hilbert space associated to a family of closable operators in the central Hilbert space. |
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