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- W2034878055 abstract "Normed spaces which are isomorphic to subspaces of the nonstandard hull of a given normed space are characterized. As a consequence it is shown that a normed space is <italic>B</italic>-convex if and only if the nonstandard hull contains no subspace isomorphic to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l 1> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{l_1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a Banach space is super-reflexive if and only if the nonstandard hull is reflexive. Also, embeddings of second dual spaces into the nonstandard hull are studied. In particular, it is shown that the second dual space of a normed space <italic>E</italic> is isometric to a complemented subspace of the nonstandard hull of <italic>E</italic>." @default.
- W2034878055 created "2016-06-24" @default.
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- W2034878055 date "1974-01-01" @default.
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- W2034878055 title "Subspaces of the nonstandard hull of a normed space" @default.
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- W2034878055 doi "https://doi.org/10.1090/s0002-9947-1974-0365098-7" @default.
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