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: 0392-4041

Abstract

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.