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Almost Periodic Type Group Actions on Compact Quantum Metric Spaces

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Abstract

A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L. We give some characterizations of almost periodic type group actions on a compact quantum metric space (A, L) by means of several kinds of subsets of A, its induced equicontinuous actions on several important subsets of the dual Banach space A*, and the Lip-norm L with its induced metric space structures on the states space \(\cal{S}(A)\) of A.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Mathematics, MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles, Nan**g University of Aeronautics and Astronautics, Nan**g, 211106, P. R. China

    Bo Tao Long

  2. School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, P. R. China

    Wei Wu

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  1. Bo Tao Long
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  2. Wei Wu
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Correspondence to Bo Tao Long.

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Conflict of Interest The authors declare no conflict of interest.

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Supported by National Natural Science Foundation of China (Grant No. 11801177), Postdoctoral Science Foundation of China (Grant No. 2020M671471) and Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000)

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Long, B.T., Wu, W. Almost Periodic Type Group Actions on Compact Quantum Metric Spaces. Acta. Math. Sin.-English Ser. 40, 568–594 (2024). https://doi.org/10.1007/s10114-023-1519-x

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  • DOI: https://doi.org/10.1007/s10114-023-1519-x

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