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 -summand vectors in Banach spaces |
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| Authors: | Antonio Aizpuru Francisco Javier Garcia-Pacheco |
| Institution: | Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, 11510, Spain ; Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242 |
| Abstract: | The aim of this paper is to study the set  of all  -summand vectors of a real Banach space  . We provide a characterization of  -summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an  -sum of a Hilbert space and a Banach space without nontrivial  -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces. |
| Keywords: | $\mathsf{L}^{\mathtt{2}}$-summand vector smoothness Hilbert space |
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