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A bound-two isomorphism between $ C(X)$ Banach spaces


Author: H. B. Cohen
Journal: Proc. Amer. Math. Soc. 50 (1975), 215-217
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1975-0380379-5
MathSciNet review: 0380379
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Abstract: Nonhomeomorphic compact Hausdorff spaces $ X$ and $ Y$ and an isomorphism $ \phi :C(X) \to C(Y)$ (onto) are constructed such that $ \vert\vert\phi \vert\vert\;\vert\vert{\phi ^{ - 1}}\vert\vert = 2$. Amir had asked if such a $ \phi $ exists with $ \vert\vert\phi \vert\vert\;\vert\vert{\phi ^{ - 1}}\vert\vert < 3$.


References [Enhancements On Off] (What's this?)

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  • [2] Michael Cambern, On isomorphisms with small bound, Proc. Amer. Math. Soc. 18 (1967), 1062-1066. MR 36 #669. MR 0217580 (36:669)
  • [3] -, Isomorphisms of $ {C_0}(Y)$ onto $ C(X)$, Pacific J. Math. 35 (1970), 307-312. MR 0433201 (55:6180)
  • [4] Y. Gordon, On the distance coefficient between isomorphic function spaces, Israel J. Math. 8 (1970), 391-397. MR 42 #5021. MR 0270128 (42:5021)
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DOI: https://doi.org/10.1090/S0002-9939-1975-0380379-5
Article copyright: © Copyright 1975 American Mathematical Society

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