Asymmetric decompositions of vectors in $JB\sp *$-algebras
Siddiqui, Akhlaq A.
Archivum Mathematicum, Tome 042 (2006), p. 159-166 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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 $tsr\ 1$.

Publié le : 2006-01-01
Classification:  17C65,  46K70,  46L70 
@article{107992,
     author = {Akhlaq A. Siddiqui},
     title = {Asymmetric decompositions of vectors in $JB\sp *$-algebras},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {159-166},
     zbl = {1164.46342},
     mrnumber = {2240353},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107992}
}

Siddiqui, Akhlaq A. Asymmetric decompositions of vectors in $JB\sp *$-algebras. Archivum Mathematicum, Tome 042 (2006) pp. 159-166. http://gdmltest.u-ga.fr/item/107992/

Jacobson N. Structure and representations of Jordan algebras, AMS Providence, Rhode Island, 1968. (1968) | MR 0251099 | Zbl 0218.17010

Kadison R. V.; Pedersen G. K. Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266. (1985) | MR 0832356 | Zbl 0573.46034

Rudin W. Functional analysis, McGraw-Hill, New York, 1973. (1973) | MR 0365062 | Zbl 0253.46001

Siddiqui A. A. Positivity of invertibles in unitary isotopes of $JB^{*}$-algebras, Preprint.

Siddiqui A. A. Self-adjointness in unitary isotopes of $JB^{*}$-algebras, Preprint. | MR 2263481 | Zbl 1142.46020

Siddiqui A. A. $JB^{*}$-algebras of $tsr\ 1$, Preprint. | Zbl 1227.46036

Wright J. D. M. Jordan $C^{*}$-algebras, Mich. Math. J. 24 (1977), 291–302. (1977) | MR 0487478 | Zbl 0384.46040

Youngson M. A. A Vidav theorem for Banach Jordan algebras, Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–272. (1978) | MR 0493372 | Zbl 0392.46038