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Extensions of Asymmetric Norms to Linear Spaces
Garcìa-Raffi, L.M.
Romaguera, S.
Sánchez Pérez, E.A.
2001
Abstract
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
33 (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.
Languages
en
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