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
Recommended Citation
Barik, Sibaprasad; Das, B. Krishna; and Sarkar, Jaydeb, "Isometric dilations and von Neumann inequality for finite rank commuting contractions" (2020). Journal Articles. 36.
https://digitalcommons.isical.ac.in/journal-articles/36
Comments
Open Access, Green