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arXiv · 1312.1371

Rigged Hilbert spaces and contractive families of Hilbert spaces

Giorgia Bellomonte·Camillo Trapani
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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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Giorgia Bellomonte, Camillo Trapani. 2013-12-04. Rigged Hilbert spaces and contractive families of Hilbert spaces. https://doi.org/10.1007/s00605-010-0249-1

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