Asymmetric decompositions of vectors in J B * -algebras

Akhlaq A. Siddiqui

Archivum Mathematicum (2006)

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

Abstract

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By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital J B * -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 J B * -algebras of t s r 1 .

How to cite

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Siddiqui, 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

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  1. Jacobson N., Structure and representations of Jordan algebras, AMS Providence, Rhode Island, 1968. (1968) Zbl0218.17010MR0251099
  2. Kadison R. V., Pedersen G. K., Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266. (1985) Zbl0573.46034MR0832356
  3. Rudin W., Functional analysis, McGraw-Hill, New York, 1973. (1973) Zbl0253.46001MR0365062
  4. Siddiqui A. A., Positivity of invertibles in unitary isotopes of J B * -algebras, Preprint. 
  5. Siddiqui A. A., Self-adjointness in unitary isotopes of J B * -algebras, Preprint. Zbl1142.46020MR2263481
  6. Siddiqui A. A., J B * -algebras of t s r 1 , Preprint. Zbl1227.46036
  7. Wright J. D. M., Jordan C * -algebras, Mich. Math. J. 24 (1977), 291–302. (1977) Zbl0384.46040MR0487478
  8. 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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