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Uniformly convex spaces, bead spaces, and equivalence conditions

Lech Pasicki (2011)

Czechoslovak Mathematical Journal

The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the...

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

Rychter, Jan (2000)

Serdica Mathematical Journal

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.

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 ℓ p ( L p ' ) formés des fonctions appartenant localement à L p ' et qui ont un comportement ℓ p à l’infini.

Uniqueness of Cartesian Products of Compact Convex Sets

Zbigniew Lipecki, Viktor Losert, Jiří Spurný (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X i , i∈ I, and Y j , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of ∏ i ∈ I X i onto ∏ j ∈ J Y j . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of X i onto Y b ( i ) , i∈ I.

Uniqueness of complete norms for quotients of Banach function algebras

W. Bade, H. Dales (1993)

Studia Mathematica

We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra L 1 ( G ) of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients A ( Γ ) / J ( E ) ¯ arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed. We construct...

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