$\mathsf {L}^{\mathtt {2}}$-summand vectors in Banach spaces
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- by Antonio Aizpuru and Francisco Javier Garcia-Pacheco PDF
- Proc. Amer. Math. Soc. 134 (2006), 2109-2115 Request permission
Abstract:
The aim of this paper is to study the set $\mathsf {L} _{X}^{\mathtt {2}}$ of all $\mathsf {L}^{\mathtt {2}}$-summand vectors of a real Banach space $X$. We provide a characterization of $\mathsf {L}^{\mathtt { 2}}$-summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an $\mathsf {L}^{\mathtt {2}}$-sum of a Hilbert space and a Banach space without nontrivial $\mathsf {L}^{\mathtt {2}}$-summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.References
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Additional Information
- Antonio Aizpuru
- Affiliation: Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, 11510, Spain
- Email: antonio.aizpuru@uca.es
- Francisco Javier Garcia-Pacheco
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: fgarcia@math.kent.edu
- Received by editor(s): December 1, 2004
- Received by editor(s) in revised form: January 31, 2005, and February 18, 2005
- Published electronically: January 17, 2006
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2109-2115
- MSC (2000): Primary 46B20, 46C05, 46B04
- DOI: https://doi.org/10.1090/S0002-9939-06-08243-8
- MathSciNet review: 2215781