Quantum duality, unbounded operators, and inductive limits


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Dosi A.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.51, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 6
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1063/1.3419771
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS

Özet

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]