| Title:
|
On vectorial inner product spaces (English) |
| Author:
|
Marques, João de Deus |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
539-550 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $E$ be a real linear space. A vectorial inner product is a mapping from $E\times E$ into a real ordered vector space $Y$ with the properties of a usual inner product. Here we consider $Y$ to be a $\mathcal B$-regular Yosida space, that is a Dedekind complete Yosida space such that $\bigcap _{J\in {\mathcal B}}J=\lbrace 0 \rbrace $, where $\mathcal B$ is the set of all hypermaximal bands in $Y$. In Theorem 2.1.1 we assert that any $\mathcal B$-regular Yosida space is Riesz isomorphic to the space $B(A)$ of all bounded real-valued mappings on a certain set $A$. Next we prove Bessel Inequality and Parseval Identity for a vectorial inner product with range in the $\mathcal B$-regular and norm complete Yosida algebra $(B(A),\sup _{\alpha \in A}|x(\alpha )|)$. (English) |
| MSC:
|
46A19 |
| MSC:
|
46C50 |
| idZBL:
|
Zbl 1079.46503 |
| idMR:
|
MR1777475 |
| . |
| Date available:
|
2009-09-24T10:35:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127591 |
| . |
| Reference:
|
[1] E. Coimbra: Aproximação em Espaços V-Métricos.Ph.D. Thesis, Dept. Mathematics, FCT, UNL, 1979. |
| Reference:
|
[2] W. A. J. Luxemburg, A. C. Zaanen: Riesz Spaces I.North-Holland, 1971. |
| Reference:
|
[3] J. D. Marques: Normas Vectoriais e Espaços V-Métricos.P.A.P.C.C., FCT, UNL, 1988. |
| Reference:
|
[4] J. D. Marques: Normas Vectoriais Hermíticas com Valores em Álgebras de Yosida $\mathcal B$-Regulares.Ph.D. Thesis, Dept. Mathematics, FCT, UNL, 1993. |
| Reference:
|
[5] J. D. Marques: A Representation Theorem in Vectorially Normed Spaces.Trabalhos de Investigação - No. 1 Dept. Mathematics, FCT, UNL, 1995. Zbl 0851.46004, MR 1377735 |
| Reference:
|
[6] F. Robert: Étude et Utilization de Normes Vectorielles en Analyse Numérique Linéaire.These Grenoble, 1968. |
| Reference:
|
[7] A. C. Zaanen: Riesz Spaces II.North Holland, 1983. Zbl 0519.46001, MR 0704021 |
| . |
