Journal of Operator Theory

Volume 92, Issue 1, Summer 2024 pp. 49-76.

Pairs of commuting pure contractions and isometric dilation

Authors: Srijan Sarkar
Author institution: Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

Summary: In this paper, we study the question: \textit{does a pair of commuting pure contractions always dilate to a pair of commuting pure isometries?} We report certain progress by proving that pairs of commuting pure contractions with finite dimensional defect spaces and pairs of commuting pure partial isometries always dilate to pairs of commuting pure isometries. Our method is based on an explicit structure of isometric dilation for pure pairs of commuting contractions obtained recently by {B.K. Das, J. Sarkar, S. Sarkar}, \textit{Adv. Math.} \textbf{322}(2017), 186--200.

DOI: http://dx.doi.org/10.7900/jot.2022jul30.2386
Keywords: pure contractions, pair of commuting contractions, pure isometries, pair of commuting isometries, Hardy space, Ando dilation, von Neumann inequality

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