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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: antonio.aizpuru@uca.es
FRANCISCO J GARCÍA-PACHECO
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio, 44242, The United States e-mail: fgarcia@math.kent.edu
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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

REFERENCES

1.Aizpuru, A. and García-Pacheco, F. J., L2-summand vectors in Banach spaces, Proc. Amer. Math. Soc. 134 (7) (2006), 2109–2115.CrossRefGoogle Scholar
2.Aizpuru, A. and García-Pacheco, F. J., L2-summand vectors and complemented hilbertizable subspaces, Boll. Unione Mat. Ital. 10–B (8) (2007), 1143–1148.Google Scholar
3.Aron, R. M., Gurariy, V. I. and Seoane, J. B., Lineability and spaceability of sets of functions on ℝ, Proc. Amer. Math. Soc. 133 (3) (2005), 795–803.CrossRefGoogle Scholar
4.Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, in Pitman monographs and surveys in pure and applied mathematics 64 (Longman, Harlow, UK, 1993).Google Scholar
5.Megginson, R. E., An introduction to Banach space theory, in Graduate texts in mathematics 183 (New York, Springer-Verlag, 1998).CrossRefGoogle Scholar