Displaying similar documents to “Reflexive Banach spaces without equivalent norms which are uniformly convex or uniformly differentiable in every direction”

Rotund and uniformly rotund Banach spaces.

V. Montesinos, J. R. Torregrosa (1991)

Collectanea Mathematica

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In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

Lancien, Gilles (1995)

Serdica Mathematical Journal

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We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for...

On regularization in superreflexive Banach spaces by infimal convolution formulas

Manuel Cepedello-Boiso (1998)

Studia Mathematica

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We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex C 1 , α functions converging to f uniformly on bounded...

Near smoothness of Banach spaces.

Józef Banas, Kishin Sadarangani (1995)

Collectanea Mathematica

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The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.