Comptes Rendus
no. 10
Functional Analysis
Quantized moment problem
[Sur le problème du moment quantifié]

Présenté par : Gilles Pisier

Anar Dosiev1
1 Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey
Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 627-630.

Dans cette Note nous développons la technique des espaces fractionnaires dans le cadre d'espaces d'opérateurs locaux. Le résultat principal est une variante du théorème non commutatif d'Albrecht–Vasilescu sur les extensions, lequel implique une solution du problème du moment quantifié.

In this Note we develop the fractional space technique in the local operator space framework. As the main result we present the noncommutative Albrecht–Vasilescu extension theorem, which in turn solves the quantized moment problem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.03.022
Anar Dosiev 1

1 Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey 
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Anar Dosiev. Quantized moment problem. Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 627-630. doi : 10.1016/j.crma.2007.03.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.022/

[1] E. Albrecht, F.-H. Vasilescu, Unbounded extensions and operator moment problems, Preprint, 2004

[2] A.A. Dosiev, The representation theorem for local operator spaces, Funct. Anal. Appl. (2007), in press

[3] E.G. Effros; C. Webster Operator analogues of locally convex spaces, Samos, 1996 (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.), Volume vol. 495 (1997)

[4] F.-H. Vasilescu Operator moment problems in unbounded sets, Operator Theory: Advances and Applications, vol. 127, Birkhäuser, Basel, 2001, pp. 613-638

[5] F.-H. Vasilescu Spaces of fractions and positive functionals, Math. Scand., Volume 96 (2005), pp. 257-279

[6] F.-H. Vasilescu, Unbounded normal algebras and spaces of fractions, in: Proceedings of Conference “Operator Theory, System Theory and Scattering Theory: Multidimensional Generalizations and Related Topics”, Beer-Sheva, 2005

[7] C. Webster, Local operator spaces and applications, Ph.D. University of California, Los Angeles, 1997

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