Displaying similar documents to “On strong proximinality in normed linear spaces”

Bidual Spaces and Reflexivity of Real Normed Spaces

Keiko Narita, Noboru Endou, Yasunari Shidama (2014)

Formalized Mathematics

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In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear...

On the non-existence of norms for some algebras of functions

Bertram Yood (1994)

Studia Mathematica

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Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for Ω = ℝ n where ℝ is the reals.

On the lambda-property and computation of the lambda-function of some normed spaces.

Mohamed Akkouchi, Hassan Sadiky (1993)

Extracta Mathematicae

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R. M. Aron and R. H. Lohman introduced, in [1], the notion of lambda-property in a normed space and calculated the lambda-function for some classical normed spaces. In this paper we give some more general remarks on this lambda-property and compute the lambda-function of other normed spaces, namely: B(S,∑,X) and M(E).

Chebyshev coficients for L-preduals and for spaces with the extension property.

José Manuel Bayod Bayod, María Concepción Masa Noceda (1990)

Publicacions Matemàtiques

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We apply the Chebyshev coefficients λ and λ, recently introduced by the authors, to obtain some results related to certain geometric properties of Banach spaces. We prove that a real normed space E is an L-predual if and only if λ(E) = 1/2, and that if a (real or complex) normed space E is a P space, then λ(E) equals λ(K), where K is the ground field of E.

A universal modulus for normed spaces

Carlos Benítez, Krzysztof Przesławski, David Yost (1998)

Studia Mathematica

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We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.

Characterizations of Rotundity and Smoothness by Approximate Orthogonalities

Tomasz Stypuła, Paweł Wójcik (2016)

Annales Mathematicae Silesianae

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In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of dual spaces.