Dana Fraňková (2019)
Mathematica Bohemica
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This paper deals with regulated functions having values in a Banach space. In particular, families of equiregulated functions are considered and criteria for relative compactness in the space of regulated functions are given.
Antonio S. Granero, Mar Jiménez, Alejandro Montesinos, José P. Moreno, Anatolij Plichko (2003)
Studia Mathematica
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Stanisław Szufla (2009)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Leandro Candido, Elói Medina Galego (2012)
Fundamenta Mathematicae
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For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...
K. Goebel, E. Złotkiewicz (1971)
Colloquium Mathematicae
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Jochen Reinermann (1970)
Annales Polonici Mathematici
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Stanisław Szufla (1977)
Annales Polonici Mathematici
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J. R. Holub (1971)
Colloquium Mathematicae
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V. Lakshmikantham, A. R. Mitchell, R. W. Mitchell (1978)
Annales Polonici Mathematici
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Gasparis, I., Papadiamantis, M. K., Zisimopoulou, D. Z. (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 05D10, 46B03. Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.