Quantum duality, unbounded operators, and inductive limits

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2010-06-01

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Dosi, Anar

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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 G-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. 2010 American Institute of Physics. [doi:10.1063/1.3419771]

Subject Keywords

Mathematical Physics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/64176

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.3419771

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Natural Sciences and Mathematics, Article

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Citation Formats

A. Dosi, “Quantum duality, unbounded operators, and inductive limits,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64176.