Abstract
In order to obtain a rigorous version of the Dirac formulation of quantum mechanics, one has to go beyond Hilbert space and one usually resorts to a Rigged Hilbert space (RHS). However, this is a particular case of partial inner product spaces (pip-spaces), a general formalism that also generalizes many families of function spaces that play a central role in analysis. In this paper, we shall give an overview of pip-spaces and operators on them, defined globally. We will also discuss a number of operator classes, such as morphisms and projections.
Mathematics Subject Classification (2010). Primary 46C50; Secondary 47A70, 47B37, 47B38.
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Antoine, JP. (2013). Partial Inner Product Spaces, a Unifying Language for Quantum Mechanics. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_13
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DOI: https://doi.org/10.1007/978-3-0348-0448-6_13
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