Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

FREE PRODUCTS OF OPERATOR SYSTEMS

  • Pop, Florin (Department of Mathematics Wagner College)
  • Received : 2021.05.18
  • Accepted : 2021.11.08
  • Published : 2022.05.31
Download PDF
⟨ Previous Next ⟩

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

References

  1. D. Avitzour, Free products of C*-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423-435. https://doi.org/10.2307/1998890
  2. 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
  3. 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
  4. 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.
  5. 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
  6. 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
  7. 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
  8. 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
  9. N. Ozawa, On the lifting property for universal C*-algebras of operator spaces, J. Operator Theory 46 (2001), no. 3, suppl., 579-591.
  10. V. Paulsen, Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, Cambridge, 2002.
  11. 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.
  12. 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
  13. F. Pop, Notes on a theorem of Ozawa, unpublished manuscript, available at https://www.researchgate.net/profile/Florin_Pop2