| Title:
|
Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces (English) |
| Author:
|
Şerb, Ioan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
107-119 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus $\mu_{_X}$ of the normed space $X$. The values of the rectangular modulus at some noteworthy points are well-known constants of $X$. Characterizations (involving $\mu_{_X})$ of inner product spaces of dimension $\geq 2$, respectively $\geq 3$, are given and the behaviour of $\mu_{_X}$ is studied. (English) |
| Keyword:
|
characterizations of inner product spaces |
| Keyword:
|
orthogonality |
| Keyword:
|
moduli of Banach spaces |
| MSC:
|
46B04 |
| MSC:
|
46B20 |
| MSC:
|
46C15 |
| idZBL:
|
Zbl 1060.46506 |
| idMR:
|
MR1715205 |
| . |
| Date available:
|
2009-01-08T18:50:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119066 |
| . |
| Reference:
|
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