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Displaying 241 –
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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...
*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.
Some class of locally solid topologies (called uniformly -continuous) on Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly -continuous topologies in terms of some family of pseudonorms is given. The finest uniformly -continuous topology on the Orlicz-Bochner space is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).
Étude des propriétés des unions et intersections d’espaces relatifs à un ensemble de mesures positives sur un groupe commutatif localement compact lorsque 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 formés des fonctions appartenant localement à et qui ont un comportement à l’infini.
Let , i∈ I, and , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of onto . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of onto , i∈ I.
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 of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients 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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