Rigid OLpstructures of non-commutative Lp-spaces associated with hyperfinite von Neumann algebras

Authors

  • Marius Junge
  • Zhong-Jin Ruan
  • Quanhua Xu

DOI:

https://doi.org/10.7146/math.scand.a-14945

Abstract

This paper is devoted to the study of rigid local operator space structures on non-commutative Lp-spaces. We show that for 1p2<, a non-commutative Lp-space Lp(M) is a rigid OLp space (equivalently, a rigid COLp space) if and only if it is a matrix orderly rigid OLp space (equivalently, a matrix orderly rigid COLp space). We also show that Lp(M) has these local properties if and only if the associated von Neumann algebra M is hyperfinite. Therefore, these local operator space properties on non-commutative Lp-spaces characterize hyperfinite von Neumann algebras.

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Published

2005-03-01

How to Cite

Junge, M., Ruan, Z.-J., & Xu, Q. (2005). Rigid OLpstructures of non-commutative Lp-spaces associated with hyperfinite von Neumann algebras. MATHEMATICA SCANDINAVICA, 96(1), 63–95. https://doi.org/10.7146/math.scand.a-14945

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Section

Articles