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Uniform approximation theorems for real-valued continuous functions.

M. Isabel Garrido, Francisco Montalvo (1991)

Extracta Mathematicae

For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform...

Uniform convexity and associate spaces

Petteri Harjulehto, Peter Hästö (2018)

Czechoslovak Mathematical Journal

We prove that the associate space of a generalized Orlicz space L φ ( · ) is given by the conjugate modular φ * even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling Φ -function is equivalent to a doubling Φ -function. As a consequence, we conclude that L φ ( · ) is uniformly convex if φ and φ * are weakly doubling.

Uniform G-Convexity for Vector-Valued Lp Spaces

Boyko, Nataliia, Kadets, Vladimir (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B20.Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).

Uniformly μ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces

Krzysztof Feledziak (1998)

Commentationes Mathematicae Universitatis Carolinae

Some class of locally solid topologies (called uniformly μ -continuous) on Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly μ -continuous topologies in terms of some family of pseudonorms is given. The finest uniformly μ -continuous topology 𝒯 I ϕ ( X ) on the Orlicz-Bochner space L ϕ ( X ) is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).

Unions et intersections d’espaces L p invariantes par translation ou convolution

Jean-Paul Bertrandias, Christian Datry, Christian Dupuis (1978)

Annales de l'institut Fourier

Étude des propriétés des unions et intersections d’espaces L p ( s ) relatifs à un ensemble S de mesures positives sur un groupe commutatif localement compact lorsque S est invariant par translation ou stable par convolution.Dans des cas particuliers, on retrouve les propriétés d’espaces étudiés par A. Beurling et par B. Koremblium.On étudie aussi les espaces p ( L p ' ) formés des fonctions appartenant localement à L p ' et qui ont un comportement p à l’infini.

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