Title: On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces
Author(s): E. J. Atto, V.S.K. Assiamoua, Y. Mensah
Pages: 123-135
Cite as:
E. J. Atto, V.S.K. Assiamoua, Y. Mensah, On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces, Int. J. Anal. Appl., 5 (2) (2014), 123-135.


We define a particular space of bounded linear maps using a Von Neumann algebra and some operator spaces. By this, we prove some isomorphisms, and using interpolation in some particular cases, we get analogue of non-commutative Lp spaces.

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  1. J. Bergh and J. Lfstrm, Interpolation spaces. Springer-Verlag, Berlin, 1976. Google Scholar

  2. D. Blecher and V. Paulsen, Tensor products of operators spaces. J. Funct. Anal. 99 (1991) 262-292. Google Scholar

  3. D. Blecher, The standard dual of an operator space. Pacific J. Math. 153 (1992) 15-30. Google Scholar

  4. J. Dixmier, Formes linaires sur un anneau d’oprateurs. Bull. Soc. Math. France 81 (1953) 9-39. Google Scholar

  5. E. Effros and Z. J. Ruan, A new approach to operator spaces. Canadian Math. Bull. 34 (1991) 329-337. Google Scholar

  6. E. Effros and Z. J. Ruan, Recent development in operator spaces. Current Topics in operator Algebras. Proceedings of the ICM-90 Satelite Conference held in Nara (August 1990). World Sci. Publishing, River Edge, N. J., 1991, p146-164. Google Scholar

  7. E. Effros and Z. J. Ruan, On the abstract characterization of operator spaces. Proc. Amer. Math. Soc. 119 (1993) 579-584. Google Scholar

  8. H. Kosaki, Applications of the complex interpolation method to a Von Neumann algebra: non-commutative Lp-spaces. J. Funct. Anal. 56 (1984) 29-78. Google Scholar

  9. R. Kunze, Lp Fourier transforms on locally compact unimodular groups. Trans. Amer. Math. Soc. 89 (1958) 519-540. Google Scholar

  10. G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms. Memoirs Amer. Math. Soc. vol. 122, 585 (1996) 1-103. Google Scholar

  11. G. Pisier, Non-commutative vector valued Lp-spaces and completely p-summing maps. Ast´erisque (Soc. Math. France) 247 (1998), 1-131. Google Scholar

  12. Z. J. Ruan, Subspaces of C∗−algebras. J. Funct. anal. 76 (1988)217-230. Google Scholar

  13. I. Segal, A non-commutative extension of abstract extension. Ann. of Math. 57 (1953) 401- 457. Google Scholar

  14. W. Stinespring, Integration theorem for gages and duality for unimodular groups. Trans. Amer. Math. Soc. 90 (1959) 15-26. Google Scholar

  15. Q. Xu, Operator spaces and non-commutative Lp. The part on non-commutative Lp-spaces. Lectures in the Summer School on Banach spaces and Operator spaces, Nankai University -China, July 16 - July 20, 2007. Google Scholar


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