On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 513-520
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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.
@article{BUMI_2007_8_10B_3_a0,
author = {Alsina, C. and Tom\'as, M.S.},
title = {On some {Orthogonality} {Relations} in {Real} {Normed} {Spaces} and {Characterizations} of {Inner} {Products}},
journal = {Bollettino della Unione matematica italiana},
pages = {513--520},
publisher = {mathdoc},
volume = {Ser. 8, 10B},
number = {3},
year = {2007},
zbl = {1183.46023},
mrnumber = {2351525},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a0/}
}
TY - JOUR AU - Alsina, C. AU - Tomás, M.S. TI - On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products JO - Bollettino della Unione matematica italiana PY - 2007 SP - 513 EP - 520 VL - 10B IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a0/ LA - en ID - BUMI_2007_8_10B_3_a0 ER -
%0 Journal Article %A Alsina, C. %A Tomás, M.S. %T On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products %J Bollettino della Unione matematica italiana %D 2007 %P 513-520 %V 10B %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a0/ %G en %F BUMI_2007_8_10B_3_a0
Alsina, C.; Tomás, M.S. On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 513-520. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a0/