[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b210392

FREE PRODUCTS OF OPERATOR SYSTEMS

Pop, Florin (Department of Mathematics Wagner College)

Publication Information

Bulletin of the Korean Mathematical Society / v.59, no.3, 2022 , pp. 659-669 More about this Journal

Abstract

In this paper we introduce the notion of universal free product for operator systems and operator spaces, and prove extension results for the operator system lifting property (OSLP) and operator system local lifting property (OSLLP) to the universal free product.

Keywords

Operator system; completely positive map; free product;

Citations & Related Records

Reference

1	E. Kirchberg, On nonsemisplit extensions, tensor products and exactness of group C*-algebras, Invent. Math. 112 (1993), no. 3, 449-489. https://doi.org/10.1007/BF01232444 DOI
2	A. Kavruk, V. I. Paulsen, I. G. Todorov, and M. Tomforde, Tensor products of operator systems, J. Funct. Anal. 261 (2011), no. 2, 267-299. https://doi.org/10.1016/j.jfa.2011.03.014 DOI
3	G. Pisier, A simple proof of a theorem of Kirchberg and related results on C*-norms, J. Operator Theory 35 (1996), no. 2, 317-335.
4	D. Avitzour, Free products of C*-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423-435. https://doi.org/10.2307/1998890 DOI
5	E. Kirchberg and S. Wassermann, C*-algebras generated by operator systems, J. Funct. Anal. 155 (1998), no. 2, 324-351. https://doi.org/10.1006/jfan.1997.3226 DOI
6	V. Paulsen, Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, Cambridge, 2002.
7	F. Boca, A note on full free product C*-algebras, lifting and quasidiagonality, in Operator theory, operator algebras and related topics (Timi,soara, 1996), 51-63, Theta Found., Bucharest, 1997.
8	F. Boca, Free products of completely positive maps and spectral sets, J. Funct. Anal. 97 (1991), no. 2, 251-263. https://doi.org/10.1016/0022-1236(91)90001-L DOI
9	F. Boca, Completely positive maps on amalgamated product C*-algebras, Math. Scand. 72 (1993), no. 2, 212-222. https://doi.org/10.7146/math.scand.a-12445 DOI
10	A. S. Kavruk, V. I. Paulsen, I. G. Todorov, and M. Tomforde, Quotients, exactness, and nuclearity in the operator system category, Adv. Math. 235 (2013), 321-360. https://doi.org/10.1016/j.aim.2012.05.025 DOI
11	F. Pop, On the double commutant expectation property for operator systems, Oper. Matrices 9 (2015), no. 1, 165-179. https://doi.org/10.7153/oam-09-09 DOI
12	F. Pop, Notes on a theorem of Ozawa, unpublished manuscript, available at https://www.researchgate.net/profile/Florin_Pop2
13	N. Ozawa, On the lifting property for universal C*-algebras of operator spaces, J. Operator Theory 46 (2001), no. 3, suppl., 579-591.