| Title:
|
$n$-inner product spaces and projections (English) |
| Author:
|
Misiak, Aleksander |
| Author:
|
Ryż, Alicja |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
87-97 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is a continuation of investigations of $n$-inner product spaces given in \cite{five,six,seven} and an extension of results given in \cite{three} to arbitrary natural $n$. It concerns families of projections of a given linear space $L$ onto its $n$-dimensional subspaces and shows that between these families and $n$-inner products there exist interesting close relations. (English) |
| Keyword:
|
$n$-inner product space |
| Keyword:
|
$n$-normed space |
| Keyword:
|
$n$-norm of projection |
| MSC:
|
46C05 |
| MSC:
|
46C50 |
| idZBL:
|
Zbl 0970.46013 |
| idMR:
|
MR1752081 |
| DOI:
|
10.21136/MB.2000.126265 |
| . |
| Date available:
|
2009-09-24T21:40:33Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126265 |
| . |
| Reference:
|
[1] C. Diminnie S. Gähler A. White: 2-inner product spaces.Demonstratio Math. 6 (1973), 525-536. MR 0365099 |
| Reference:
|
[2] S. Gähler: Lineare 2-normierte Räume.Math. Nachr. 28 (1965), 1-43. MR 0169021, 10.1002/mana.19640280102 |
| Reference:
|
[3] S. Gähler Z. Żekanowski: Tensors, 2-inner products and projections.Demonstratio Math. 19 (1986), 747-766. MR 0902931 |
| Reference:
|
[4] S. Gähler Z. Żekanowski: Remarks on tensors and families of projections.Math. Nachr. 143 (1989), 277-290. MR 1018248, 10.1002/mana.19891430121 |
| Reference:
|
[5] A. Misiak: n-inner product spaces.Math. Nachr. 140 (1989), 299-319. Zbl 0708.46025, MR 1015402, 10.1002/mana.19891400121 |
| Reference:
|
[6] A. Misiak: Orthogonality and orthonormality in n-inner product spaces.Math. Nachr. 143 (1989), 249-261. Zbl 0708.46025, MR 1018246, 10.1002/mana.19891430119 |
| Reference:
|
[7] A. Misiak: Simple n-inner product spaces.Prace Naukowe Politechniki Szczecińskiej 12 (1991), 63-74. Zbl 0754.15027 |
| Reference:
|
[8] Z. Żekanowski: On some generalized 2-inner products in the Riemannian manifolds.Demonstratio Math. 12 (1979), 833-836. MR 0560371 |
| . |
