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Quantum duality, unbounded operators, and inductive limits

Dosi, Anar
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Abstract

In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with S-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of operator spaces are used to introduce locally compact and locally trace class unbounded operators on a quantum domain and prove the dual realization theorem for an abstract quantum space.

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS97 MATHEMATICS AND COMPUTINGBANACH SPACECOMMUTATION RELATIONSDUALITYFIELD THEORIESFUNCTIONSHILBERT SPACEMATHEMATICAL OPERATORSMATHEMATICAL SPACEMATHEMATICSMATRICESQUANTIZATIONSPACETOPOLOGY

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Dosi, Anar. 2010-06-15. Quantum duality, unbounded operators, and inductive limits. https://doi.org/10.1063/1.3419771

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