A new proof of a Lemma by Phelps.
Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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Francisco Javier García-Pacheco (2015)
Open Mathematics
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In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted...
Robert A. McGuigan, Jr. (1970)
Compositio Mathematica
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Joan Wick Pelletier, Robert D. Rosebrugh (1979)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Nygaard, Olav (2002)
International Journal of Mathematics and Mathematical Sciences
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J. Väisälä (1992)
Studia Mathematica
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We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.
Bogdan Rzepecki (1979)
Annales Polonici Mathematici
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H. G. Dales
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We modify the very well known theory of normed spaces (E,||·||) within functional analysis by considering a sequence (||·||ₙ: n ∈ ℕ) of norms, where ||·||ₙ is defined on the product space Eⁿ for each n ∈ ℕ. Our theory is analogous to, but distinct from, an existing theory of ’operator spaces’; it is designed to relate to general spaces for p ∈ [1,∞], and in particular to L¹-spaces, rather than to L²-spaces. After recalling in Chapter 1 some results in functional analysis, especially...
Ciesielski, K., Moslehian, M.S. (2010)
Annals of Functional Analysis (AFA) [electronic only]
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