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# On $C^*$-algebra generated by Fock representation of Wick algebra with braided coefficients

### Abstract

We consider $C^*$-algebras $\mathcal{W}(T)$ generated by operators of Fock representations of Wick $*$-algebras with a braided coefficient operator $T$. It is shown that for any braided $T$ with $||T||<1$ one has the inclusion $\mathcal{W}(0)\subset\mathcal{W}(T)$. Conditions for existence of an isomorphism $\mathcal{W}(T)\simeq\mathcal{W}(0)$ are discussed.

### Article Information

 Title On $C^*$-algebra generated by Fock representation of Wick algebra with braided coefficients Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 2, 168-173 MathSciNet MR2849476 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

D. Proskurin
Kyiv Taras Shevchenko University, Cybernetics Department, 64 Volodymyrska, Kyiv, 01033, Ukraine

### Citation Example

D. Proskurin, On $C^*$-algebra generated by Fock representation of Wick algebra with braided coefficients, Methods Funct. Anal. Topology 17 (2011), no. 2, 168-173.

### BibTex

@article {MFAT586,
AUTHOR = {Proskurin, D.},
TITLE = {On $C^*$-algebra generated by Fock representation of Wick algebra with braided coefficients},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {2},
PAGES = {168-173},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=586},
}