Open Accessđť–«^{2}-summand vectors in Banach spaces
Author(s) -
A. Aizpuru,
Francisco Javier GarcĂaPacheco
Publication year - 2006
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-06-08243-8
Subject(s) - algorithm , annotation , artificial intelligence , computer science , mathematics
The aim of this paper is to study the set L X 2 \mathsf {L} _{X}^{\mathtt {2}} of all L 2 \mathsf {L}^{\mathtt {2}} -summand vectors of a real Banach space X X . We provide a characterization of L 2 \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 L 2 \mathsf {L}^{\mathtt {2}} -sum of a Hilbert space and a Banach space without nontrivial L 2 \mathsf {L}^{\mathtt {2}} -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.