Results 1 to 10 of about 402 (231)
Asymmetric Normed Baire Space [PDF]
Results in Mathematics, 2021 We prove that an asymmetric normed space is never a Baire space if the topology induced by the asymmetric norm is not equivalent to the topology of a norm. More precisely, we show that a biBanach asymmetric normed space is a Baire space if and only if it is isomorphic to its associated normed space.
Mohammed Bachir
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Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space [PDF]
Results in Mathematics, 2022 [EN] We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov. These results generalize those obtained by Romaguera et al.
Carmen Alegre
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Index of symmetry and topological classification of asymmetric normed spaces [PDF]
Rocky Mountain Journal of Mathematics, 2020 Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space. The aim of this note is to prove, using the Baire category theorem, that if Lc(X, Y) is a vector space for some asymmetric normed space Y , then X is isomorphic to its associated ...
Mohammed Bachir, Gonzalo Flores
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The weak topology in finite dimensional asymmetric normed spaces [PDF]
Topology and Its Applications, 2019 [EN] In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the same as the topology of the asymmetric norm. We provide a class of finite dimensional asymmetric normed spaces where both topologies coincide. We also prove that the weak topology of an
Carmen Alegre
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Compactness and finite dimension in asymmetric normed linear spaces
Topology and Its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L M Garcia-Raffi
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Journal of Numerical Analysis and Approximation Theory, 2003 A well known result of R. R. Phelps (1960) asserts that in order that every linear continuous functional, defined on a subspace \(Y\) of a real normed space \(X\), have a unique norm preserving extension it is necessary and sufficient that its ...
Costică Mustăţa
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Extension of bounded linear functionals and best approximation in spaces with asymmetric norm
Journal of Numerical Analysis and Approximation Theory, 2004 The present paper is concerned with the characterization of the elements of best approximation in a subspace \(Y\) of a space with asymmetric norm, in terms of some linear functionals vanishing on \(Y\).
Ş. Cobzaş, C. Mustăţa
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The Uniform Boundedness Theorem in Asymmetric Normed Spaces [PDF]
Abstract and Applied Analysis, 2012 We obtain a uniform boundedness type theorem in the frame of asymmetric normed spaces. The classical result for normed spaces follows as a particular case.
Alegre, C., Romaguera, S., Veeramani, P.
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Functional Analysis in Asymmetric Normed Spaces [PDF]
Frontiers in Mathematics, 2013 Stefan Cobzaş
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Compact bilinear operators on asymmetric normed spaces [PDF]
Topology and its Applications, 2022 The paper is concerned with compact bilinear operators on asymmetric normed spaces. The study of multilinear operators on asymmetric normed spaces was initiated by Latreche and Dahia, Colloq. Math. (2020). We go further in this direction and prove a Schauder type theorem on the compactness of the adjoint of a compact bilinear operator and study the ...
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