On norm-preserving isomorphisms of \(L^p(\mu, H)\) (Q2818401)
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scientific article; zbMATH DE number 6624879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On norm-preserving isomorphisms of \(L^p(\mu, H)\) |
scientific article; zbMATH DE number 6624879 |
Statements
7 September 2016
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vector-valued function spaces
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projections
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linear surjective isometries
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On norm-preserving isomorphisms of \(L^p(\mu, H)\) (English)
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For a \(\sigma\)-finite complete measure space \((\Omega, {\mathcal A},\mu)\), for a Hilbert space \(H\) and for \(1\leq p <\infty\), surjective linear isometries of the space of Bochner-integrable functions \(L^p(\mu,H)\) were described by \textit{P. Greim} [Bull. Aust. Math. Soc. 27, 121--128 (1983; Zbl 0496.46023)]. In this article, the authors obtain a similar description when the measure space has a perfect positive measure. This is a different proof than the one given earlier by the second author [Turk. J. Math. 23, No. 3, 389--399 (1999; Zbl 0997.46030)].
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