On unitary convex decompositions of vectors in a J B * -algebra

Akhlaq A. Siddiqui

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 2, page 79-86
  • ISSN: 0044-8753

Abstract

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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 J B * -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 J B * -algebras.

How to cite

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Siddiqui, Akhlaq A.. "On unitary convex decompositions of vectors in a $JB^{*}$-algebra." Archivum Mathematicum 049.2 (2013): 79-86. <http://eudml.org/doc/260627>.

@article{Siddiqui2013,
abstract = {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.},
author = {Siddiqui, Akhlaq A.},
journal = {Archivum Mathematicum},
keywords = {$C^\{*\}$-algebra; $JB^\{*\}$-algebra; unit ball; invertible element; unitary element; unitary isotope; convex hull; unitary rank; unitary convex decomposition; -algebra; JB-algebra; unit ball; invertible element; unitary element; unitary isotope; convex hull; unitary rank; unitary convex decomposition},
language = {eng},
number = {2},
pages = {79-86},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On unitary convex decompositions of vectors in a $JB^\{*\}$-algebra},
url = {http://eudml.org/doc/260627},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Siddiqui, Akhlaq A.
TI - On unitary convex decompositions of vectors in a $JB^{*}$-algebra
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 2
SP - 79
EP - 86
AB - 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.
LA - eng
KW - $C^{*}$-algebra; $JB^{*}$-algebra; unit ball; invertible element; unitary element; unitary isotope; convex hull; unitary rank; unitary convex decomposition; -algebra; JB-algebra; unit ball; invertible element; unitary element; unitary isotope; convex hull; unitary rank; unitary convex decomposition
UR - http://eudml.org/doc/260627
ER -

References

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  1. Braun, R., Kaup, W., Upmeier, H., 10.1007/BF01214510, Math. Z. 161 (1978), 277–290. (1978) Zbl0385.32002MR0493373DOI10.1007/BF01214510
  2. Jacobson, N., Structure and representations of Jordan algebras, AMS Providence, Rhode Island, 1968. (1968) Zbl0218.17010MR0251099
  3. Kadison, R. V., Pedersen, G. K., Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266. (1985) Zbl0573.46034MR0832356
  4. Rørdam, M., The theory of unitary rank and regular approximation, Ph.D. thesis, University of Pennsylvania, 1987. (1987) 
  5. Rørdam, M., Advances in the theory of unitary rank and regular approximations, Ann. of Math. (2) 128 (1988), 153–172. (1988) MR0951510
  6. Siddiqui, A. A., Computation of the λ u –function in J B * –algebras, submitted. 
  7. Siddiqui, A. A., Asymmetric decompositions of vectors in J B * –algebras, Arch. Math. (Brno) 42 (2006), 159–166. (2006) Zbl1164.46342MR2240353
  8. Siddiqui, A. A., On unitaries in J B * –algebras, Indian J. Math. 48 (1) (2006), 35–48. (2006) Zbl1115.46058MR2229466
  9. Siddiqui, A. A., 10.1007/s00013-006-1718-6, Arch. Math. 87 (2006), 350–358. (2006) Zbl1142.46020MR2263481DOI10.1007/s00013-006-1718-6
  10. Siddiqui, A. A., 10.3792/pjaa.83.176, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), 176–178. (2007) Zbl1207.46046MR2376600DOI10.3792/pjaa.83.176
  11. Siddiqui, A. A., 10.1155/2007/37186, Int. J. Math. Math. Sci. 2007 (2007), 24. (2007) MR2306360DOI10.1155/2007/37186
  12. Siddiqui, A. A., A proof of the Russo–Dye theorem for J B * –algebras, New York J. Math. 16 (2010), 53–60. (2010) Zbl1231.46015MR2645985
  13. Siddiqui, A. A., Convex combinations of unitaries in J B * –algebras, New York J. Math. 17 (2011), 127–137. (2011) Zbl1227.46035MR2781910
  14. Siddiqui, A. A., The λ u –function in J B * –algebras, New York J. Math. 17 (2011), 139–147. (2011) Zbl1227.46036MR2781911
  15. Wright, J. D. M., Jordan C * –algebras, Michigan Math. J. 24 (1977), 291–302. (1977) Zbl0384.46040MR0487478
  16. Youngson, M. A., 10.1017/S0305004100055092, Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–272. (1978) Zbl0392.46038MR0493372DOI10.1017/S0305004100055092

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