Dilations and rigid factorisations on noncommutative L^p-spaces

2008/03/31 by Junge, Marius, Merdy, Christian Le · 1 citation
#46L07 #46L51 #48B28 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0803.4410

Abstract

We study some factorisation and dilation properties of completely positive maps on noncommutative L^p-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (=commutative) L^p-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier's operator space valued noncommutative L^p-spaces that we investigate in the first part of the paper.

Cited by

• Moment kernels, nested defects, and Cuntz dilations

Related

• N Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on L^p-spaces
• Positive contractive projections on noncommutative L^p-spaces and nonassociative L^p-spaces
• Ando dilations and inequalities on noncommutative varieties
• Dilation properties of measurable Schur multipliers and Fourier multipliers
• The positive contractive part of a Noncommutative L^p-space is a complete Jordan invariant