Quantum duality, unbounded operators, and inductive limits

2010/06/01 by Anar Dosi · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory

paper · doi:10.1063/1.3419771

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.

Citations

• Local operator spaces, unbounded operators and multinormed C * -algebras

Cited by

• Separable morphisms of operator Hilbert systems, Pietsch factorizations and entanglement breaking maps

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