Rigid OL~p structures of non-commutative L~p-spaces associated with hyperfinite von Neumann algebras
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Autores: Z.-J. Ruan, Marius Junge
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 1, 2005, págs. 63-95
- Idioma: inglés
- DOI: 10.7146/math.scand.a-14945
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Resumen
his paper is devoted to the study of rigid local operator space structures on non-commutative Lp-spaces. We show that for 1≤p≠2<∞, 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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