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Projective Tensor Products of <i> C*</i>-Algebras
Department of Mathematics, University of Delhi, Delhi, India
Department of Mathematics, University of Delhi, Delhi, India
- 1 Department of Mathematics, University of Delhi, Delhi, India
- 2 Department of Mathematics, University of Delhi, Delhi, India
Advances in Pure Mathematics·Volume 04 (2014)·Pages 176–188·Published 5 May 2014·DOI10.4236/apm.2014.45023
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Abstract
For C* -algebras A and B , the constant involved in the canonical embedding of into is shown to be . We also consider the corresponding operator space version of this embedding. Ideal structure of is obtained in case A or B has only finitely many closed ideals.
KeywordsBanach Space Projective Tensor NormOperator Space Projective Tensor Norm
- Schatten, R. (1943) On the Direct Product of Banach Spaces. Transactions of the American Mathematical Society, 53, 195-217. http://dx.doi.org/10.1090/S0002-9947-1943-0007568-7
- Kumar, A. and Sinclair, A.M. (1998) Equivalence of Norms on Operator Space Tensor Products of C*-Algebras. Transactions of the American Mathematical Society, 350, 2033-2048. http://dx.doi.org/10.1090/S0002-9947-98-02190-4
- Haagerup, U. and Musat, M. (2008) The Effros-Ruan Conjecture for Bilinear Forms on C*-Algebras. Inventiones Mathematicae, 174, 139-163. http://dx.doi.org/10.1007/s00222-008-0137-7
- Jain, R. and Kumar, A. (2011) Operator Space Projective Tensor Product: Embedding into Second Dual and Ideal Structure. Available on arXiv:1106.2644v1.
- Blecher, D.P. and LeMerdy, C. (2004) Operator Algebras and Their Modules—An Operator Space Approach. London Mathematical Society Monographs, New Series, The Clarendon Press, Oxford University Press, Oxford.
- Ryan, R. (2002) Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics, Springer-Verlag, Berlin, Heidelberg. http://dx.doi.org/10.1007/978-1-4471-3903-4
- Haagerup, U. (1985) The Grothendieck Inequality for Bilinear Forms on C*-Algebras. Advances in Mathematics, 56, 93-116. http://dx.doi.org/10.1016/0001-8708(85)90026-X
- Lance, C. (1973) On Nuclear C*-Algebras. Journal of Functional Analysis, 12, 157-176. http://dx.doi.org/10.1016/0022-1236(73)90021-9
- Archbold, R.J. and Batty, C.J.K. (1980) C*-Tensor Norms and Slice Maps. Journal of the London Mathematical Society, 22, 127-138. http://dx.doi.org/10.1112/jlms/s2-22.1.127
- Effros, E.G. and Ruan, Z-J. (2000) Operator Spaces. Claredon Press, Oxford.
- Jain, R. and Kumar, A. (2008) Operator Space Tensor Products of C*-Algebras. Mathematische Zeitschrift, 260, 805-811. http://dx.doi.org/10.1007/s00209-008-0301-1
- Kumar, A. (2001) Operator Space Projective Tensor Product of C*-Algebras. Mathematische Zeitschrift, 237, 211-217. http://dx.doi.org/10.1007/PL00004864
- Itoh, T. (2000) Completely Positive Decompositions from Duals of C*-Algebras to Von Neumann Algebras. Mathematica Japonica, 51, 89-98.
- Effros, E.G. and Ruan, Z-J. (1992) On Approximation Properties for Opertaor Spaces. International Journal of Mathematics, 1, 163-187. http://dx.doi.org/10.1142/S0129167X90000113