Positive contractive projections on noncommutative ${\mathrm{L}}^p$-spaces and nonassociative ${\mathrm{L}}^p$-spaces

Abstract

We continue our investigation of contractive projections on noncommutative ${\mathrm{L}}^p$-spaces where $1<p<\infty$ started in \cite{ArR19}. We improve the results of \cite{ArR19} and we characterize precisely the positive contractive projections on a noncommutative ${\mathrm{L}}^p$-space associated with a $\sigma$-finite von Neumann algebra. We connect this topic to the theory of ${\mathrm{JW}}^{\ast }$-algebras. More precisely, in large cases, we are able to show that the range of a positive contractive projection is isometric to a nonassociative ${\mathrm{L}}^p$-space associated to a ${\mathrm{JW}}^{\ast }$-algebra.

32 pages

Cited by in corpus (1)

• 2-positive contractive projections on noncommutative ${\mathrm{L}}^p$-spaces