Isometric dilations and von Neumann inequality for a class of Tuples in the polydisc

Authors

Sibaprasad Barik, Indian Institute of Technology Bombay
B. Krishna Das, Indian Institute of Technology Bombay
Kalpesh J. Haria, Indian Institute of Technology Mandi
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Transactions of the American Mathematical Society

Abstract

The celebrated Sz.-Nagy and Foias and Ando theorems state that a single contraction, or a pair of commuting contractions, acting on a Hilbert space always possesses isometric dilation and subsequently satisfies the von Neumann inequality for polynomials in C[z] or C[z1, z2], respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for n-tuples, n ≥ 3, of commuting contractions. The goal of this paper is to provide a taste of isometric dilations, von Neumann inequality, and a refined version of von Neumann inequality for a large class of n-tuples, n≥3, of commuting contractions.

First Page

1429

Last Page

1450

DOI

10.1090/tran/7676

Publication Date

1-1-2019

Comments

Open Access, Bronze, Green

Recommended Citation

Barik, Sibaprasad; Krishna Das, B.; Haria, Kalpesh J.; and Sarkar, Jaydeb, "Isometric dilations and von Neumann inequality for a class of Tuples in the polydisc" (2019). Journal Articles. 1036.
https://digitalcommons.isical.ac.in/journal-articles/1036