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Best approximation in spaces with asymmetric norm
Journal of Numerical Analysis and Approximation Theory, 2006 In this paper we shall present some results on spaces with asymmetric seminorms, with emphasis on best approximation problems in such spaces.
Ştefan Cobzaş, 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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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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Functional Analysis in Asymmetric Normed Spaces [PDF]
Frontiers in Mathematics, 2013 Stefan Cobzaş
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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.
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New Results on the Aggregation of Norms
Mathematics, 2021 It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable.
Tatiana Pedraza +1 more
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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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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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Compactness in asymmetric normed spaces
Topology and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alegre, C. +3 more
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The Goldstine Theorem for asymmetric normed linear spaces
Topology and its Applications, 2009 If \(X\) is a linear space, then a function \(q: X\to\mathbb{R}^+\) is called an asymmetric norm on \(X\) if for all \(x,y\in X\) and \(r\in \mathbb{R}^+\), \(x= 0\) if and only if \(q(x)= q(-x)= 0\), \(q(rx)= rq(x)\) and \(q(x+ y)= q(x)+ q(y)\). It follows that the function \(q^s: X\to\mathbb{R}\) defined by \(d^s(x)= \max(q(x), q(-x))\) is a norm on \
García-Raffi, L.M. +2 more
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