Unitary dilation of freely independent contractions
Scott Atkinson, Christopher Ramsey
TL;DR
This paper extends the classical Sz.-Nagy-Foias dilation theorem to the setting of free probability, demonstrating that freely independent contractions can be dilated to freely independent unitaries.
Contribution
It introduces a dilation result for freely independent contractions, generalizing classical dilation theory to free probability.
Findings
Freely independent contractions can be dilated to freely independent unitaries.
The dilation preserves free independence in the non-commutative setting.
The result bridges classical dilation theory with free probability frameworks.
Abstract
Inspired by the Sz.-Nagy-Foias dilation theorem we show that freely independent contractions dilate to freely independent unitaries.
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