This is an announcement for the paper “On Multivariate Matsaev's Conjecture” by Samya Kumar Rayhttps://arxiv.org/find/math/1/au:+Ray_S/0/1/0/all/0/1.

Abstract: We present various multivariate generalizations of the Matsaev's conjecture in different settings, namely on $L^p$-spaces, non-commutative $L^p$-spaces and semigroups. We show that the multivariate Matsaev's conjecture holds true for any commuting tuple of isometries on $L^p$-spaces. We prove a similar result for Schatten-$p$ classes. We also show that any two parameter strongly continuous semigroup of contractions on a Hilbert space satisfies the multivariate Matsaev's conjecture for semigroups. At the end, we discuss some open questions.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.00733