| Title:
|
Tensor products of Hilbert modules over locally $C^*$-algebras (English) |
| Author:
|
Joiţa, Maria |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
727-737 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the tensor products of Hilbert modules over locally $C^{*}$-algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert $C^{*}$-modules are also valid in the context of Hilbert modules over locally $C^{*}$-algebras. (English) |
| Keyword:
|
locally $C^{*}$-algebras |
| Keyword:
|
continuous $*$-morphism |
| Keyword:
|
inverse system of Hilbert $C^{*}$-modules |
| Keyword:
|
exterior tensor product of Hilbert modules |
| Keyword:
|
interior tensor product of Hilbert modules |
| MSC:
|
46A13 |
| MSC:
|
46L08 |
| MSC:
|
46M05 |
| idZBL:
|
Zbl 1080.46523 |
| idMR:
|
MR2086729 |
| . |
| Date available:
|
2009-09-24T11:16:59Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127924 |
| . |
| Reference:
|
[1] M. Fragoulopoulou: Tensor products of enveloping locally $C^{*}$-algebras.Schriftenreihe, Univ. Münster, 1997, pp. 1–81. Zbl 0906.46040, MR 1607924 |
| Reference:
|
[2] A. Inoue: Locally $C^{*}$-algebras.Mem. Faculty Sci. Kyushu Univ. Ser. A 75 (1971), 197–235. Zbl 0227.46060, MR 0305089 |
| Reference:
|
[3] K. K. Jensen and K. Thomsen: Elements of $KK$-theory.Birhäuser-Verlag, , 1991. MR 1124848 |
| Reference:
|
[4] M. Joiţa: The stabilization theorem for Hilbert modules over locally $C^{*}$-algebras.The 3rd International Conference on Topological Algebra and Applications, (ICTAA3), Oulu, Finland, July 2–6, 2001. Zbl 1074.46041 |
| Reference:
|
[5] M. Joiţa: Strict completely positive linear maps between locally $C^{*}$-algebras and representations on Hilbert modules.J. London Math. (2) 66 (2002), 421–432. MR 1920412, 10.1112/S0024610702003411 |
| Reference:
|
[6] E. C. Lance: Hilbert $C^{*}$-modules. A toolkit for operator algebraists.London Math. Soc. Lecture Note Series 210, Cambridge Univ. Press, Cambridge, 1995. Zbl 0822.46080, MR 1325694 |
| Reference:
|
[7] A. Mallios: Hermitian $K$-theory over topological $*$-algebras.J. Math. Anal. Appl. 106 (1985), 454–539. MR 0782803, 10.1016/0022-247X(85)90122-2 |
| Reference:
|
[8] N. C. Phillips: Inverse limits of $C^{*}$-algebras.J. Operator Theory 19 (1988), 159–195. Zbl 0662.46063, MR 0950831 |
| . |
