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Noncommutative $ L_p$-space and operator system

Author: Kyung Hoon Han
Journal: Proc. Amer. Math. Soc. 137 (2009), 4157-4167
MSC (2000): Primary 46L07, 46L52, 47L07
Published electronically: July 14, 2009
MathSciNet review: 2538576
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Abstract: We show that noncommutative $ L_p$-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant $ 2^{1 \over p}$. Therefore, noncommutative $ L_p$-spaces can be embedded into $ B(H)$ $ 2^{1 \over p}$-completely isomorphically and complete order isomorphically.

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  • [CE] M.-D. Choi and E. Effros, Injectivity and operator spaces, J. Funct. Anal. 24 (1997), 156-209. MR 0430809 (55:3814)
  • [HJX] U. Haagerup M. Junge, and Q. Xu, A reduction method for noncommutative $ L_p$-spaces and applications , Trans. Amer. Math. Soc., to appear.
  • [JRX] M. Junge, Z-J. Ruan and Q. Xu, Rigid $ \mathcal{OL}_p$ structures of non-commutative $ L_p$-spaces associated with hyperfinite von Neumann algebras, Math. Scand. 96 (2005), 63-95. MR 2142873 (2006b:46086)
  • [K] H. Kosaki, Applications of the complex interpolation method to a von Neumann algebra: Non-commutative $ L^p$-spaces, J. Funct. Anal. 56 (1984), 29-78 MR 735704 (86a:46085)
  • [Pa] V. I. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, Cambridge, UK, 2002. MR 1976867 (2004c:46118)
  • [Pi1] G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. 122, No. 585, 1996. MR 1342022 (97a:46024)
  • [Pi2] G. Pisier, Non-commutative vector valued $ L_p$-spaces and completely p-summing maps, Astérisque 247, 1998. MR 1648908 (2000a:46108)
  • [S] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401-457. MR 0054864 (14:991f)
  • [Ta] M. Takesaki, Theory of Operator Algebras. II, Encyclopaedia of Mathematical Sciences, Vol. 125, Springer-Verlag, 2002. MR 1873025 (2002m:46083)
  • [Te1] M. Terp, $ L^p$ spaces associated with von Neumann algebras, Math. Institute, Copenhagen University, 1981.
  • [Te2] M. Terp, Interpolation spaces between a von Neumann algebra and its predual, J. Operator Theory 8 (1982), 327-360. MR 677418 (85b:46075)
  • [W] W. Werner, Subspaces of $ L(H)$ that are $ *$-invariant, J. Funct. Anal. 193 (2002), 207-223. MR 1929500 (2003h:46086)

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Additional Information

Kyung Hoon Han
Affiliation: Department of Mathematical Sciences, Seoul National University, San 56-1 ShinRimDong, KwanAk-Gu, Seoul 151-747, Korea

Received by editor(s): July 13, 2008
Received by editor(s) in revised form: February 16, 2009, and March 20, 2009
Published electronically: July 14, 2009
Additional Notes: This work was supported by the BK21 project of the Ministry of Education, Korea.
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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