DOI QR코드

DOI QR Code

NUCLEARITY PROPERTIES AND C*-ENVELOPES OF OPERATOR SYSTEM INDUCTIVE LIMITS

  • Kumar, Ajay (Department of Mathematics University of Delhi) ;
  • Luthra, Preeti (Department of Mathematics University of Delhi)
  • Received : 2017.05.22
  • Accepted : 2018.06.07
  • Published : 2018.09.01

Abstract

We investigate the relationship between $C^*$-envelopes and inductive limit of operator systems. Various operator system nuclearity properties of inductive limit for a sequence of operator systems are also discussed.

Keywords

References

  1. W. B. Arveson, Subalgebras of C*-algebras, Acta Math. 123 (1969), 141-224. https://doi.org/10.1007/BF02392388
  2. B. Blackadar, Operator Algebras, Encyclopaedia of Mathematical Sciences, 122, Springer-Verlag, Berlin, 2006.
  3. N. P. Brown and N. Ozawa, C*-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88, American Mathematical Society, Providence, RI, 2008.
  4. D. Farenick, A. S. Kavruk, V. I. Paulsen, and I. G. Todorov, Operator systems from discrete groups, Comm. Math. Phys. 329 (2014), no. 1, 207-238. https://doi.org/10.1007/s00220-014-2037-6
  5. V. P. Gupta and P. Luthra, Operator system nuclearity via C*-envelopes, J. Aust. Math. Soc. 101 (2016), no. 3, 356-375. https://doi.org/10.1017/S1446788716000082
  6. M. Hamana, Injective envelopes of operator systems, Publ. Res. Inst. Math. Sci. 15 (1979), no. 3, 773-785. https://doi.org/10.2977/prims/1195187876
  7. A. S. Kavruk, Nuclearity related properties in operator systems, J. Operator Theory 71 (2014), no. 1, 95-156. https://doi.org/10.7900/jot.2011nov16.1977
  8. A. S. 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
  9. 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
  10. E. Kirchberg, On subalgebras of the CAR-algebra, J. Funct. Anal. 129 (1995), no. 1, 35-63. https://doi.org/10.1006/jfan.1995.1041
  11. 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
  12. P. Luthra and A. Kumar, Embeddings and C*-envelopes of exact operator systems, Bull. Aust. Math. Soc. 96 (2017), no. 2, 274-285. https://doi.org/10.1017/S0004972717000284
  13. L. Mawhinney and I. G. Todorov, Inductive limits in the operator system and related categories, arXiv preprint arXiv:1705.04663, 2017.
  14. C. M. Ortiz and V. I. Paulsen, Lovasz theta type norms and operator systems, Linear Algebra Appl. 477 (2015), 128-147. https://doi.org/10.1016/j.laa.2015.03.022
  15. G. Pisier, Introduction to operator space theory, London Mathematical Society Lecture Note Series, 294, Cambridge University Press, Cambridge, 2003.
  16. M. Rordam, Classification of nuclear, simple C*-algebras, in Classification of nuclear C*-algebras, Entropy in operator algebras, 1-145, Encyclopaedia Math. Sci., 126, Oper. Alg. Non-commut. Geom., 7, Springer, Berlin, 2002.
  17. M. Rordam, F. Larsen, and N. Laustsen, An introduction to K-theory for C*-algebras, London Mathematical Society Student Texts, 49, Cambridge University Press, Cambridge, 2000.
  18. D. Zheng, The operator system generated by Cuntz isometries, arXiv preprint arXiv:1410.6950, 2014.