Mathematische Annalen

, 335:109

Embedding of Cq and Rq into noncommutative Lp -spaces, 1≤p<q≤2


DOI: 10.1007/s00208-005-0732-5

Cite this article as:
Xu, Q. Math. Ann. (2006) 335: 109. doi:10.1007/s00208-005-0732-5


We prove that a quotient of a subspace of CppRp (1≤p<2) embeds completely isomorphically into a noncommutative Lp -space, where Cp and Rp are respectively the p-column and p-row Hilbertian operator spaces. We also represent Cq and Rq (p<q≤2) as quotients of subspaces of CppRp. Consequently, Cq and Rq embed completely isomorphically into a noncommutative Lp (M). We further show that the underlying von Neumann algebra M cannot be semifinite.

Mathematics subject classification (2000)

Primary 46L07Secondary 47L25


embeddingp-column and p-row spacesnoncommutative Lp-spacesinterpolation

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon, cedexFrance