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Title: | Uniqueness of invariant Hahn-Banach extensions |
Authors: | Bandyopadhyay, Pradipta Roy, Ashoke K. |
Keywords: | Funcionales sublineales;Secuencias anidadas de (π-) bolas;Hahn-Banach invariante extensiones;Sublinear functionals;Nested sequences of (π-) balls;Invariant Hahn-Banach extensions |
Issue Date: | 2007 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | Let π be a linear functional on a subspace π of a real linear space π provided with a sublinear functional π with π β€ π on π. If π’ is an abelian semigroup of linear transformations π: π βπ such that π(π ) β π π (ππ) β€ π (π) and π(ππ) = π(π) for all π β π’, π β π and π β π respectively, then a generalization of the classical Hahn-Banach theorem asserts that there exists an extension π of π, π β€ π on π and π` remains invariant under π’. The present paper investigates various equivalent conditions for the uniqueness of such extensions and these are related to nested sequences of π-balls, a concept that has proved useful in recent years in dealing with such extensions. The results are illustrated by a variety of examples and applications. |
URI: | http://hdl.handle.net/10662/15602 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 22, nΒΊ 2 (2007) |
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