# Asymmetric decompositions of vectors in $J{B}^{*}$-algebras

Archivum Mathematicum (2006)

- Volume: 042, Issue: 2, page 159-166
- ISSN: 0044-8753

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topSiddiqui, Akhlaq A.. "Asymmetric decompositions of vectors in $JB^*$-algebras." Archivum Mathematicum 042.2 (2006): 159-166. <http://eudml.org/doc/249784>.

@article{Siddiqui2006,

abstract = {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 $tsr\ 1$.},

author = {Siddiqui, Akhlaq A.},

journal = {Archivum Mathematicum},

keywords = {$C^\{*\}$-algebras; Jordan algebras; $JB^\{*\}$-algebras; unitary isotopes; -algebras; Jordan algebras; unitary isotopes},

language = {eng},

number = {2},

pages = {159-166},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Asymmetric decompositions of vectors in $JB^*$-algebras},

url = {http://eudml.org/doc/249784},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Siddiqui, Akhlaq A.

TI - Asymmetric decompositions of vectors in $JB^*$-algebras

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 2

SP - 159

EP - 166

AB - 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 $tsr\ 1$.

LA - eng

KW - $C^{*}$-algebras; Jordan algebras; $JB^{*}$-algebras; unitary isotopes; -algebras; Jordan algebras; unitary isotopes

UR - http://eudml.org/doc/249784

ER -

## References

top- Jacobson N., Structure and representations of Jordan algebras, AMS Providence, Rhode Island, 1968. (1968) Zbl0218.17010MR0251099
- Kadison R. V., Pedersen G. K., Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266. (1985) Zbl0573.46034MR0832356
- Rudin W., Functional analysis, McGraw-Hill, New York, 1973. (1973) Zbl0253.46001MR0365062
- Siddiqui A. A., Positivity of invertibles in unitary isotopes of $J{B}^{*}$-algebras, Preprint.
- Siddiqui A. A., Self-adjointness in unitary isotopes of $J{B}^{*}$-algebras, Preprint. Zbl1142.46020MR2263481
- Siddiqui A. A., $J{B}^{*}$-algebras of $tsr\phantom{\rule{4pt}{0ex}}1$, Preprint. Zbl1227.46036
- Wright J. D. M., Jordan ${C}^{*}$-algebras, Mich. Math. J. 24 (1977), 291–302. (1977) Zbl0384.46040MR0487478
- Youngson M. A., A Vidav theorem for Banach Jordan algebras, Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–272. (1978) Zbl0392.46038MR0493372

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