Abstract
Let \(\Gamma ,\Delta \) be nonempty index sets, and let H, K be inner product spaces. We prove that for \(p\ge 1\) any surjective phase-isometry between \(\ell ^p(\Gamma ,H)\) and \(\ell ^p(\Delta , K)\) is a plus–minus linear isometry. This can be considered as an extension of Wigner’s theorem for real \(\ell ^p(\Gamma , H)\)-type spaces.
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Acknowledgements
The authors thank the referee whose careful reading and suggestions led to a much improved version of this paper. The authors wish to express their appreciation to Professor Guanggui Ding for several valuable comments. This work was supported by the Natural Science Foundation of China, Grant Nos. 11371201, 11201337, 11201338.
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Zeng, X., Huang, X. Phase-isometries between two \(\ell ^p(\Gamma , H)\)-type spaces. Aequat. Math. 94, 793–802 (2020). https://doi.org/10.1007/s00010-020-00723-4
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DOI: https://doi.org/10.1007/s00010-020-00723-4