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

Sibaprasad Barik, B. Krishna Das, Kalpesh J. Haria, Jaydeb Sarkar

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)1429-1450
Number of pages22
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - 1 Jan 2019
Externally publishedYes


  • Bounded analytic functions
  • Commuting contractions
  • Commuting isometries
  • Distinguished variety
  • Hardy space over the polydisc
  • Isometric dilations
  • Von Neumann inequality

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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