| Title:
|
Non-commutative Gelfand-Naimark theorem (English) |
| Author:
|
Migda, Janusz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
253-255 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that if Y is the Hausdorffization of the primitive spectrum of a $C^{\ast }$-algebra $A$ then $A$ is $\ast $-isomorphic to the $C^{\ast }$-algebra of sections vanishing at infinity of the canonical $C^{\ast }$-bundle over $Y$. (English) |
| Keyword:
|
$C^{\ast }$-algebra |
| Keyword:
|
$C^{\ast }$-bundle |
| Keyword:
|
sectional representation |
| MSC:
|
46L05 |
| MSC:
|
46L85 |
| idZBL:
|
Zbl 0809.46057 |
| idMR:
|
MR1241734 |
| . |
| Date available:
|
2009-01-08T18:03:09Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118578 |
| . |
| Reference:
|
[1] Dauns J., Hofmann K.H.: Representation of rings by sections.Mem. Amer. Math. Soc. 83 (1968). Zbl 0174.05703, MR 0247487 |
| Reference:
|
[2] Dixmier J.: Les $C^{\ast }$-algèbres et leurs representations.Gauthier-Villars, Paris, 1969. Zbl 0288.46055, MR 0246136 |
| Reference:
|
[3] Dupre M.J., Gillette M.R.: Banach bundles, Banach modules and automorphisms of $C^{\ast }$- algebras.Research Notes in Math. 92, Pitman Advanced Publishing Program, Boston- London-Melbourne, 1983. Zbl 0536.46048, MR 0721812 |
| Reference:
|
[4] Fell J.M.G.: The structure of algebras of operator fields.Acta Math. 106 (1961), 233-280. Zbl 0101.09301, MR 0164248 |
| Reference:
|
[5] Fell J.M.G.: An extension of Macley's method to Banach $\ast $-algebraic bundles.Mem. Amer. Math. Soc. 90 (1969). MR 0259619 |
| Reference:
|
[6] Tomiyama J.: Topological representations of $C^{\ast }$-algebras.Tohôku Math. J. 14 (1962), 187-204. MR 0143053 |
| . |
