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Title: Extensions of Asymmetric Norms to Linear Spaces
Authors: Garcìa-Raffi, L.M.
Romaguera, S.
Sánchez Pérez, E.A.
Keywords: asymmetric normsemilinear spaceextension
Issue Date: 2001
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: L.M. García-Raffi, S. Romaguera and E. A. Sánchez Pérez, "Extensions of Asymmetric Norms to Linear Spaces", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 33 (2001), pp. 113-125.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
33 (2001)
Let M be a subset of a (real) linear space that is closed with respect to the sum of vectors and the product by nonnegative scalars. An asymmetric seminorm on M is a nonnegative and subbaditive positively homogeneous function q defined on M. Moreover, q is an asymmetric norm if in addition for every non zero element x such that -x belongs to M, q(x) or q(-x) are different from zero. Consider the linear expansion X of M. In this paper we characterize when (M,q) can be extended to an asymmetric normed linear space $(X,q^*)$, i.e. when there exists an asymmetric norm $q^*$ on X such that $q^*\midM = q$. As an application we study these extensions in the case of subsets of normed lattices.
Type: Article
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.33 (2001)

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