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A NOTE ON L2-SUMMAND VECTORS IN DUAL SPACES

Published online by Cambridge University Press:  01 September 2008

ANTONIO AIZPURU  and
FRANCISCO J GARCÍA-PACHECO
ANTONIO AIZPURU
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, 11510, Spain e-mail: [email protected]
FRANCISCO J GARCÍA-PACHECO
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio, 44242, The United States e-mail: [email protected]
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Abstract

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It is shown that every L2-summand vector of a dual real Banach space is a norm-attaining functional. As consequences, the L2-summand vectors of a dual real Banach space can be determined by the L2-summand vectors of its predual; for every n ∈ , every real Banach space can be equivalently renormed so that the set of norm-attaining functionals is n-lineable; and it is easy to find equivalent norms on non-reflexive dual real Banach spaces that are not dual norms.

Keywords

Primary 46B2046C0546B04
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 429 - 432
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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