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Homogeneous ideals in Wick $*$-algebras

Author(s): Daniil Proskurin
Journal: Proc. Amer. Math. Soc. 126 (1998), 3371-3376.
MSC (1991): Primary 81R50, 47A62, 46L05
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Abstract: The necessary and sufficient condition for the family of homogeneous elements to determine a Wick ideal is presented. The structure of homogeneous Wick ideals with degree higher than 2 is discussed. For the braided operator $T$ a formula to calculate the largest cubic ideal when the quadratic one is known is obtained. Irreducible $*$-representations of the $\mu$-CAR algebra are classified.

References:

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P. E. T. Jørgensen, L. M. Schmitt and R. F. Werner. Positive representations of general commutation relations allowing Wick ordering. J. Funct. Anal. 134, no. 1 (1995), 33-99. MR 96h:81033

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M. Bo\.{z}ejko and R. Speicher. Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces. Mat. Ann. 300 (1994), 97-120. MR 95g:46105

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Additional Information:

Daniil Proskurin
Affiliation: Department of Mathematics, Kiev University, Kiev, Ukraine
Email: prosk@imath.kiev.ua

DOI: 10.1090/S0002-9939-98-04305-6
PII: S 0002-9939(98)04305-6
Received by editor(s): November 21, 1996
Received by editor(s) in revised form: December 10, 1996
Additional Notes: This work was partially supported by the CRDF, grant no. 292
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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V. Ostrovskyi and D. Proskurin, Operator Relations, Dynamical Systems and Representations of a Class of Wick algebras, Operator Theory and Related Topics. Proceedings of the Mark Krein International Conferention on Operator Theory and Applications (Odessa, Ukraine, 18.08.1997), Oper. Theory Adv. Appl. , vol. 118, Birkhauser Verlag, Basel, 2000, pp. 335-345. (english)

D.P. Proskurin, Yu. S. Samoilenko, Representations of Wick CCR Algebra, Spectral and Evolutionary Problems 8 (1998), 43-45. (english)

Proskurin D.P., About Positiveness of Fock Inner Product of a Certain Wick Algebras, Methods Funct. Anal. Topology (1) 5 (1999), 88-94. (english)

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