| Title:
|
Asymmetric decompositions of vectors in $JB\sp *$-algebras (English) |
| Author:
|
Siddiqui, Akhlaq A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
159-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital $JB^{*}$-algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of $JB^{*}$-algebras of $tsr\ 1$. (English) |
| Keyword:
|
$C^{*}$-algebras |
| Keyword:
|
Jordan algebras |
| Keyword:
|
$JB^{*}$-algebras |
| Keyword:
|
unitary isotopes |
| MSC:
|
17C65 |
| MSC:
|
46K70 |
| MSC:
|
46L70 |
| idZBL:
|
Zbl 1164.46342 |
| idMR:
|
MR2240353 |
| . |
| Date available:
|
2008-06-06T22:47:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107992 |
| . |
| Reference:
|
[1] Jacobson N.: Structure and representations of Jordan algebras.AMS Providence, Rhode Island, 1968. Zbl 0218.17010, MR 0251099 |
| Reference:
|
[2] Kadison R. V., Pedersen G. K.: Means and convex combinations of unitary operators.Math. Scand. 57 (1985), 249–266. Zbl 0573.46034, MR 0832356 |
| Reference:
|
[3] Rudin W.: Functional analysis.McGraw-Hill, New York, 1973. Zbl 0253.46001, MR 0365062 |
| Reference:
|
[4] Siddiqui A. A.: Positivity of invertibles in unitary isotopes of $JB^{*}$-algebras.Preprint. |
| Reference:
|
[5] Siddiqui A. A.: Self-adjointness in unitary isotopes of $JB^{*}$-algebras.Preprint. Zbl 1142.46020, MR 2263481 |
| Reference:
|
[6] Siddiqui A. A.: $JB^{*}$-algebras of $tsr\ 1$.Preprint. Zbl 1227.46036 |
| Reference:
|
[7] Wright J. D. M.: Jordan $C^{*}$-algebras.Mich. Math. J. 24 (1977), 291–302. Zbl 0384.46040, MR 0487478 |
| Reference:
|
[8] Youngson M. A.: A Vidav theorem for Banach Jordan algebras.Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–272. Zbl 0392.46038, MR 0493372 |
| . |
