Abstract
This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system, and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products. Also, the authors show that if the locally compact group is amenable, then the crossed product and the reduced crossed product are isometrically isomorphic.
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The authors thank sincerely the anonymous referees for the very thorough reading of the paper and valuable comments on improving the paper.
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This work was supported by the National Natural Science Foundation of China (No. 11971277), the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province (Nos. 2019L0742, 2019L0747), the Science and Technology Plan Project of Datong City (Nos. 2021155, 2019156) and the Doctoral Scientific Research Foundation of Shanxi Datong University (No. 2015-B-09).
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Huang, L., Guo, Y. Reduced Crossed Products of Pro-Banach Algebras. Chin. Ann. Math. Ser. B 43, 295–306 (2022). https://doi.org/10.1007/s11401-022-0318-5
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DOI: https://doi.org/10.1007/s11401-022-0318-5