On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products
Alsina, C. ; Tomás, M.S.
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 513-520 / Harvested from Biblioteca Digitale Italiana di Matematica

Using some functionals which fulfil much more general requirements than the usual axioms of inner products and by considering some weak versions of orthogonal relations in real normed spaces we find new characterizations of inner products in the cases of James and Pythagoras orthogonalities but we show that this is not the case when Birkhoff orthogonality is postulated.

Usando alcuni funzionali soddisfacenti condizioni molto più generali degli usuali assiomi dei prodotti scalari e considerando alcune deboli versioni delle relazioni di ortogonalità negli spazi reali normati, troviamo nuove caratterizzazioni dei prodotti scalari nei casi di ortogonalità di James e di Pitagora, ma non nel caso dell'ortogonalità di Birkhoff.

Publié le : 2007-10-01
@article{BUMI_2007_8_10B_3_513_0,
     author = {C. Alsina and M.S. Tom\'as},
     title = {On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {513-520},
     zbl = {1183.46023},
     mrnumber = {2351525},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_513_0}
}
Alsina, C.; Tomás, M.S. On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 513-520. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_513_0/

[1] Alsina, C. - Guijarro, P. - Tomás, M. S., On heights in real normed spaces and characterizations of inner product structures, J. Just. Math. Comput. Sci. Math. Ser., 6 (1993), 151-159. | MR 1239743 | Zbl 0816.46017

[2] Alsina, C., Guijarro, P. - Tomás, M. S., Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures, Aeq. Math., 54 (1997), 234-241. | MR 1476028 | Zbl 0906.39012

[3] Amir, D., Characterizations of inner product spaces, Basel-Boston-Stuttgart (1986). | MR 941812 | Zbl 0617.46030

[4] Precupanu, T., Characterizations of Hilbertian Norms, Boll. Un. Mat. Ital. B, 15, No. 5 (1978), 161-169. | MR 498687 | Zbl 0381.46007