Isometric Dilations of Commuting Contractions and Brehmer Positivity

Sibaprasad Barik; B. Krishna Das

doi:10.1007/s11785-022-01247-2

Isometric Dilations of Commuting Contractions and Brehmer Positivity

Sibaprasad Barik, B. Krishna Das

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It is well-known that an n-tuple (n≥ 3) of commuting contractions does not posses an isometric dilation, in general. Considering a class of n-tuple of commuting contractions satisfying certain positivity assumption, we construct their isometric dilations and consequently establish their von Neumann inequality. The positivity assumption is related to Brehmer positivity and motivated by the study of isometric dilations of operator tuples in Barik et al. (Trans Amer Math Soc 372(2):1429–1450, 2019).

Original language	English
Article number	69
Journal	Complex Analysis and Operator Theory
Volume	16
Issue number	5
DOIs	https://doi.org/10.1007/s11785-022-01247-2
State	Published - 1 Jul 2022

Keywords

Brehmer positivity
Hardy space
Isometric dilations
Regular dilations
Von Neumann inequality

ASJC Scopus subject areas

Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s11785-022-01247-2

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abstract = "It is well-known that an n-tuple (n≥ 3) of commuting contractions does not posses an isometric dilation, in general. Considering a class of n-tuple of commuting contractions satisfying certain positivity assumption, we construct their isometric dilations and consequently establish their von Neumann inequality. The positivity assumption is related to Brehmer positivity and motivated by the study of isometric dilations of operator tuples in Barik et al. (Trans Amer Math Soc 372(2):1429–1450, 2019).",

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KW - Hardy space

KW - Isometric dilations

KW - Regular dilations

KW - Von Neumann inequality

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ER -

Isometric Dilations of Commuting Contractions and Brehmer Positivity

Abstract

Keywords

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