| Title:
|
On unitary convex decompositions of vectors in a $JB^{*}$-algebra (English) |
| Author:
|
Siddiqui, Akhlaq A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
79-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital $JB^{*}$-algebra permits the vector decomposable as convex combination of fewer unitaries; certain $ C^{*}$-algebra results due to M. Rørdam have been extended to the general setting of $JB^{*}$-algebras. (English) |
| Keyword:
|
$C^{*}$-algebra |
| Keyword:
|
$JB^{*}$-algebra |
| Keyword:
|
unit ball |
| Keyword:
|
invertible element |
| Keyword:
|
unitary element |
| Keyword:
|
unitary isotope |
| Keyword:
|
convex hull |
| Keyword:
|
unitary rank |
| Keyword:
|
unitary convex decomposition |
| MSC:
|
17C65 |
| MSC:
|
46H70 |
| MSC:
|
46L70 |
| idZBL:
|
Zbl 06321150 |
| idMR:
|
MR3118865 |
| DOI:
|
10.5817/AM2013-2-79 |
| . |
| Date available:
|
2013-10-14T13:39:04Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143495 |
| . |
| Reference:
|
[1] Braun, R., Kaup, W., Upmeier, H.: A holomorphic characterization of Jordan $C^{*}$–algebras.Math. Z. 161 (1978), 277–290. Zbl 0385.32002, MR 0493373, 10.1007/BF01214510 |
| Reference:
|
[2] Jacobson, N.: Structure and representations of Jordan algebras.AMS Providence, Rhode Island, 1968. Zbl 0218.17010, MR 0251099 |
| Reference:
|
[3] 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:
|
[4] Rørdam, M.: The theory of unitary rank and regular approximation.Ph.D. thesis, University of Pennsylvania, 1987. |
| Reference:
|
[5] Rørdam, M.: Advances in the theory of unitary rank and regular approximations.Ann. of Math. (2) 128 (1988), 153–172. MR 0951510 |
| Reference:
|
[6] Siddiqui, A. A.: Computation of the $\lambda _{u}$–function in $JB^{*}$–algebras.submitted. |
| Reference:
|
[7] Siddiqui, A. A.: Asymmetric decompositions of vectors in $JB^{*}$–algebras.Arch. Math. (Brno) 42 (2006), 159–166. Zbl 1164.46342, MR 2240353 |
| Reference:
|
[8] Siddiqui, A. A.: On unitaries in $JB^{*}$–algebras.Indian J. Math. 48 (1) (2006), 35–48. Zbl 1115.46058, MR 2229466 |
| Reference:
|
[9] Siddiqui, A. A.: Self–adjointness in unitary isotopes of $JB^{*}$–algebras.Arch. Math. 87 (2006), 350–358. Zbl 1142.46020, MR 2263481, 10.1007/s00013-006-1718-6 |
| Reference:
|
[10] Siddiqui, A. A.: Average of two extreme points in $JBW^{*}$–triples.Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), 176–178. Zbl 1207.46046, MR 2376600, 10.3792/pjaa.83.176 |
| Reference:
|
[11] Siddiqui, A. A.: $JB^{*}$–algebras of topological stable rank $1$.Int. J. Math. Math. Sci. 2007 (2007), 24. MR 2306360, 10.1155/2007/37186 |
| Reference:
|
[12] Siddiqui, A. A.: A proof of the Russo–Dye theorem for $JB^{*}$–algebras.New York J. Math. 16 (2010), 53–60. Zbl 1231.46015, MR 2645985 |
| Reference:
|
[13] Siddiqui, A. A.: Convex combinations of unitaries in $JB^{*}$–algebras.New York J. Math. 17 (2011), 127–137. Zbl 1227.46035, MR 2781910 |
| Reference:
|
[14] Siddiqui, A. A.: The $\lambda _{u}$–function in $JB^{*}$–algebras.New York J. Math. 17 (2011), 139–147. Zbl 1227.46036, MR 2781911 |
| Reference:
|
[15] Wright, J. D. M.: Jordan $C^{*}$–algebras.Michigan Math. J. 24 (1977), 291–302. Zbl 0384.46040, MR 0487478 |
| Reference:
|
[16] Youngson, M. A.: A Vidav theorem for Banach Jordan algebras.Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–272. Zbl 0392.46038, MR 0493372, 10.1017/S0305004100055092 |
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