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.
Bellomonte, G., Trapani, C. (2011). Rigged Hilbert spaces and contractive families of Hilbert spaces. MONATSHEFTE FÜR MATHEMATIK, 164(3), 271-285 [10.1007/s00605-010-0249-1].
Rigged Hilbert spaces and contractive families of Hilbert spaces.
BELLOMONTE, Giorgia;TRAPANI, Camillo
2011-01-01
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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