Title

Isometric dilations and von Neumann inequality for finite rank commuting contractions

Article Type

Research Article

Publication Title

Bulletin des Sciences Mathematiques

Abstract

Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of commutant lifting theorem, we introduce a class, denoted by Pn(H), of n-tuples of commuting contractions on a Hilbert space H. We always assume that n≥3. The importance of this class of n-tuples stems from the fact that the von Neumann inequality or the existence of isometric dilation does not hold in general for n-tuples, n≥3, of commuting contractions on Hilbert spaces (even in the level of finite dimensional Hilbert spaces). Under some rank-finiteness assumptions, we prove that tuples in Pn(H) always admit explicit isometric dilations and satisfy a refined von Neumann inequality in terms of algebraic varieties in the closure of the unit polydisc in Cn.

DOI

10.1016/j.bulsci.2020.102915

Publication Date

12-1-2020

Comments

Open Access, Green

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