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Isometric dilations of commuting contractions and Brehmer positivity

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arxiv 2004.12610 v1 pith:ZBQWY2TE submitted 2020-04-27 math.FA

Sibaprasad Barik , B. Krishna Das This is my paper · ORCID
classification math.FA
keywords isometricpositivitycommutingcontractionsdilationsassumptionbrehmertuple
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abstract

It is well-known that an $n$-tuple $(n\ge 3)$ 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 [4].

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