| Title:
|
$C^\ast$-algebras of operators in non-archimedean Hilbert spaces (English) |
| Author:
|
Alvarez, J. Antonio |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
573-580 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show several examples of n.a\. valued fields with involution. Then, by means of a field of this kind, we introduce ``n.a\. Hilbert spaces'' in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed. (English) |
| Keyword:
|
non-archimedean Hilbert space |
| Keyword:
|
non-archimedean $C^\ast $-algebra |
| MSC:
|
46C05 |
| MSC:
|
46L05 |
| MSC:
|
46S10 |
| MSC:
|
47S10 |
| idZBL:
|
Zbl 0784.46063 |
| idMR:
|
MR1240177 |
| . |
| Date available:
|
2009-01-08T17:58:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118527 |
| . |
| Reference:
|
[1] Alvarez García J.A.: Involutions on non-archimedean fields and algebras.Actas XIII Jornadas Hispano-Lusas de Matemáticas, Valladolid, 1988, to appear. |
| Reference:
|
[2] Bayod Bayod J.M.: Productos internos en espacios normados no arquimedianos.Doctoral dissertation, Universidad de Bilbao, 1976. |
| Reference:
|
[3] Keller H.A.: Measures on orthomodular vector space lattices.Studia Mathematica 88 (1988), 183-195. Zbl 0656.46051, MR 0931041 |
| Reference:
|
[4] Keller H.A.: Measures on infinite-dimensional orthomodular spaces.Foundations of Physics 20 (1990), 575-604. MR 1060623 |
| Reference:
|
[5] Monna A.F.: Analyse non-Archimedienne.Springer-Verlag, 1970. Zbl 0207.12402, MR 0295033 |
| Reference:
|
[6] Murphy G.J.: Commutative non-archimedean $C^\ast $-algebras.Pacific J. Math. 78 (1978), 433-446. Zbl 0393.46054, MR 0519764 |
| Reference:
|
[7] Narici L., Beckenstein E., Bachman G.: Functional Analysis and Valuation Theory.Marcel Dekker, 1971. Zbl 0218.46004, MR 0361697 |
| Reference:
|
[8] Paschke W.L.: Inner product modules over $B^\ast $-algebras.Trans. Amer. Math. Soc. 182 (1973), 443-468. Zbl 0239.46062, MR 0355613 |
| Reference:
|
[9] Rooij A.C.M. Van: Nonarchimedean Functional Analysis.Marcel Dekker, 1978. |
| . |
