On the isometries of spaces of Hölder continuous functions
A. Tromba (1976)
Studia Mathematica
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A. Tromba (1976)
Studia Mathematica
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S. Heinrich (1981)
Fundamenta Mathematicae
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Robert A. McGuigan, Jr. (1970)
Compositio Mathematica
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M. Cambern (1965)
Studia Mathematica
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Rafael Villa (1998)
Studia Mathematica
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We prove that some Banach spaces X have the property that every Banach space that can be isometrically embedded in X can be isometrically and linearly embedded in X. We do not know if this is a general property of Banach spaces. As a consequence we characterize for which ordinal numbers α, β there exists an isometric embedding between and .
Patrick N. Dowling (2000)
Collectanea Mathematica
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We obtain refinement of a result of Partington on Banach spaces containing isomorphic copies of l-∞. Motivated by this result, we prove that Banach spaces containing asymptotically isometric copies of l-∞ must contain isometric copies of l-∞.
M. Kadec (1971)
Studia Mathematica
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Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)
Colloquium Mathematicae
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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...
Jerry Johnson, John Wolfe (1979)
Studia Mathematica
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Dirk Werner, Wend Werner (1987)
Studia Mathematica
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Åsvald Lima, Eve Oja (1999)
Studia Mathematica
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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...