On non-surjective coarse isometries between Banach spaces |
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Authors: | Lixin Cheng Quanqing Fang Sijie Luo Longfa Sun |
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Institution: | 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China. E-Mail 815045306@qq.com;3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China. E-Mail sijieluo@qq.com;4. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China. E-Mail 364898029@qq.com |
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Abstract: | Assume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that if then there is a linear isometry U : X → Y so that
where ![/></span> is defined by</p><p xmlns:mml=](/na101/home/literatum/publisher/tandf/journals/content/tqma20/2019/tqma20.v042.i03/16073606.2018.1448900/20190416/images/medium/tqma_a_1448900_ilg0003.gif) Representation properties of coarse isometries in free ultrafilter limits on ![/></span> are also discussed.</td>
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Keywords: | Primary 46B04 46B20 47A58 Secondary 46A20 |
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