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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Communicated by Karlheinz Gröchenig.
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Bellomonte, G., Trapani, C. Rigged Hilbert spaces and contractive families of Hilbert spaces. Monatsh Math 164, 271–285 (2011). https://doi.org/10.1007/s00605-010-0249-1
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DOI: https://doi.org/10.1007/s00605-010-0249-1