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Unique Hahn-Banach theorems for spaces of homogeneous polynomials

Part of: Measures, integration, derivative, holomorphy Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

R. Aron ,
C. Boyd  and
Y. S. Choi
R. Aron
Affiliation:
Department of Mathematics Kent State UniversityKent Ohio 44242USA e-mail: aron@mcs.kent.edu
C. Boyd
Affiliation:
Department of Mathematics University College DublinBelfield Dublin 4Ireland e-mail: Christopher.Boyd@ucd.ie
Y. S. Choi
Affiliation:
Department of Mathematics Pohang University of Science and TechnologyPohang 790South Korea e-mail: mathchoi@posmath.postech.ac.kr
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Abstract

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We investigate certain norm and continuity conditions that provide us with ‘uniqe Hahn-Banch Theorems’ from (nc0) to (nℓ∞) and from N(nE) to N(nE″). We show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on complex c0 to ℓ∈ but there is no unique norm-preserving extension from (3c0) to (3ℓ∈).

MSC classification

Secondary: 46G25: (Spaces of) multilinear mappings, polynomials 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 387 - 400
Copyright
Copyright © Australian Mathematical Society 2001

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