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Banach algebra dynamical systems

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Abstract

This paper generalizes the C*-dynamical system to the Banach algebra dynamical system (A,G, α) and define the crossed product A ⋊α G of a given Banach algebra dynamical system (A,G, α). Then the representation of A ⋊α G is described when A admits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A ⋊α,r G and discuss the question when ⋊α G coincides with ⋊α,r G.

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Authors and Affiliations

  1. Department of Mathematics, Fudan University, Shanghai, 200433, China

    Dong Li & Shengzhi Xu

Authors
  1. Dong Li
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  2. Shengzhi Xu
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Correspondence to Dong Li.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 10971023) and the Shanghai Natural Science Foundation of China (No. 09ZR1402000).

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Li, D., Xu, S. Banach algebra dynamical systems. Chin. Ann. Math. Ser. B 35, 285–300 (2014). https://doi.org/10.1007/s11401-014-0821-4

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  • DOI: https://doi.org/10.1007/s11401-014-0821-4

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