On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products

C. Alsina; M.S. Tomás

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 513-520
  • ISSN: 0392-4033

Abstract

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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.

How to cite

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Alsina, C., and Tomás, M.S.. "On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 513-520. <http://eudml.org/doc/290376>.

@article{Alsina2007,
abstract = {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.},
author = {Alsina, C., Tomás, M.S.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {513-520},
publisher = {Unione Matematica Italiana},
title = {On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products},
url = {http://eudml.org/doc/290376},
volume = {10-B},
year = {2007},
}

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 dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 513
EP - 520
AB - 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.
LA - eng
UR - http://eudml.org/doc/290376
ER -

References

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  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. Zbl0816.46017MR1239743
  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. Zbl0906.39012MR1476028DOI10.1007/BF02755458
  3. AMIR, D., Characterizations of inner product spaces, Basel-Boston-Stuttgart (1986). Zbl0617.46030MR941812DOI10.1007/978-3-0348-5487-0_11
  4. PRECUPANU, T., Characterizations of Hilbertian Norms, Boll. Un. Mat. Ital. B, 15, No. 5 (1978), 161-169. Zbl0381.46007MR498687

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