On Multivariate Matsaev's Conjecture

Abstract

In this article, we study multivariate generalizations of the Matsaev's conjecture in commutative and non-commutative $L^p$-spaces.We prove that the multivariate analogue of Matsaev's conjecture is eventually false for all $1<p<\infty .$ We exhibit various joint dilation results on non-commutative $L^p$-spaces.

19 pages. This is well-written version and many corrections have been made. Commutativity of the unitary operators in the dilation theorem is explained

References in corpus (1)

• The von Neumann inequality for 3x3 matrices