In this paper, we show a necessary and sufficient condition for a real Banach space to have an infinite dimensional subspace which is hilbertizable and complemented using techniques related to -summand vectors.
In questo articolo, mostriamo una condizione necessaria e sufficiente affinché uno spazio di Banach reale abbia un sottospazio infinito dimensionale il quale sia hilbertizzabile e complementato, usando tecniche relazionate con vettori -summand.
@article{BUMI_2007_8_10B_3_1143_0,
author = {Antonio Aizpuru and Francisco J. Garc\'\i a-Pacheco},
title = {$L^2$-Summand Vectors and Complemented Hilbertizable Subspaces},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {10-A},
year = {2007},
pages = {1143-1148},
zbl = {1200.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_1143_0}
}
Aizpuru, Antonio; García-Pacheco, Francisco J. $L^2$-Summand Vectors and Complemented Hilbertizable Subspaces. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 1143-1148. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_1143_0/
[1] - , -summand vectors in Banach spaces, Proc. Amer. Math. Soc., 134, 7 (2006), 2109-2115. | MR 2215781
[2] et al., -structure in real Banach spaces, Lecture Notes in Mathematics 613, Berlin-Heidelberg-New York, Springer-Verlag, 1977. | MR 626051 | Zbl 0362.46020
[3] , -struktur in Banachräumen, Studia Math., 55 (1976), 71-85. | MR 402466
[4] - , Transitivity of the norm on Banach spaces, Extracta Math., 17, 1 (2002) 1-58. | MR 1914238 | Zbl 1006.46007
[5] - , A characterization of inner product spaces, Math. Japonica, 23, 4 (1978), 371-373. | MR 524986 | Zbl 0395.46018