| Title:
|
Characterizations of inner product spaces through an isosceles trapezoid property (English) |
| Author:
|
Alsina, C. |
| Author:
|
Cruells, P. |
| Author:
|
Tomás, M. S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
21-27 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained. (English) |
| Keyword:
|
inner product space |
| Keyword:
|
norm derivative $\rho ^{\prime }_{\pm }$ |
| Keyword:
|
heights |
| MSC:
|
46C15 |
| idZBL:
|
Zbl 1050.46507 |
| idMR:
|
MR1684520 |
| . |
| Date available:
|
2008-06-06T22:22:31Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107682 |
| . |
| Reference:
|
[1] Alsina C., Guijarro P., Tomás M. S.: On heights in real normed spaces and characterizations of inner product structures.Jour. Int. Math. & Comp. Sci. Vol. 6, N. 2(1993), 151-159. Zbl 0816.46017, MR 1239743 |
| Reference:
|
[2] Alsina C., Guijarro P., Tomás M. S.: A characterization of inner product spaces based on a property of height’s transform.Archiv der Mathematik Vol. 61(1993), 560-566. MR 1254068 |
| Reference:
|
[3] Alsina C., Cruells P., Tomás M. S.: Isosceles Trapezoids, Norms and Inner Products.Archiv der Mathematik (1999) Zbl 0928.46010, MR 1671283 |
| Reference:
|
[4] Amir D.: Characterizations of inner product spaces.Birkhäuser Verlag (1986). Zbl 0617.46030, MR 0897527 |
| Reference:
|
[5] Suzuki F.: A Certain Property of an Isosceles Trapezoid and its Application to Chain Circle Problems.Mathematics Magazine Vol. 8, N. 2, pp 136-145 (1995). Zbl 0877.51017, MR 1333815 |
| . |
