Banach–Stone theorems for spaces of vector bundle continuous sections

Kawamura, Kazuhiro

doi:10.1016/j.topol.2017.01.023

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Cited by 4 publications

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“…Historically, the property of a space being strictly convex has been part of the hypotheses in many of the vector‐valued Banach–Stone theorems, including that of Jerison mentioned above, see for instance .…”

Section: Introductionmentioning

confidence: 99%

Isomorphisms of spaces with large distortion

Galego

Silva

2018

Mathematische Nachrichten

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Letand be locally compact Hausdorff spaces and let be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism from 0 ( , ) onto 0 ( , ) satisfyingthen and are homeomorphic. Here ( ) denotes the Schäffer constant of . Even for the classical cases = , 1 < < ∞ and ≥ 2, this result is the -valued Banach-Stone theorem via isomorphism with the largest distortion that is known so far, namely ( ) = min { 2 1∕ , 2 1−1∕ } . On the other hand, it is well known that this result is not true for = , even though and are compact Hausdorff spaces. K E Y W O R D S 0 ( , ) spaces, spaces, Schäffer constant, strictly convex spaces, vector-valued Banach-Stone theorems M S C ( 2 0 1 0 ) Primary: 46B03, 46E15; Secondary: 46B25, 46E40 996

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Section: Introductionmentioning

confidence: 99%