A characterization of norm compactness in the Bochner space \(L^{p}(G;B)\) for an arbitrary locally compact group \(G\) (Q855419)
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| Language | Label | Description | Also known as |
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| English | A characterization of norm compactness in the Bochner space \(L^{p}(G;B)\) for an arbitrary locally compact group \(G\) |
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A characterization of norm compactness in the Bochner space \(L^{p}(G;B)\) for an arbitrary locally compact group \(G\) (English)
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7 December 2006
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Let \(G\) be a locally compact group, not necessarily Abelian, with left invariant Haar measure \(\mu\), and let \(B\) be a Banach space. Necessary and sufficient conditions are given for a subset \(\Gamma\) of the Bochner space \(L^p(G;B)\) to be relatively norm compact. This result generalizes essentially that by \textit{N.\,Dinculeanu} and \textit{J.\,K.\thinspace Brooks} [Adv.\ Math.\ 45, 255--258 (1982; Zbl 0532.46024)].
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Bochner space
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compactness
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locally compact group
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Haar measure
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