Research Article

Extensions and dilations of module maps

Published in: Quaestiones Mathematicae
Volume 45 , issue 10 , 2022 , pages: 1629–1640

DOI: 10.2989/16073606.2021.1967502

Author(s): Massoud Amini Tarbiat Modares University, Iran

Keywords: Primary: 47A20 , Secondary: 46L07 , Operator algebras , dilations , injectivity , operator modules , completely positive maps , extensions

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Abstract

We study completely positive module maps on C*-algebras which are C*-module over another C*-algebra with compatible actions. We extend several well known dilation and extension results to this setup, including the Stinespring dilation theorem and Wittstock, Arveson, and Voiculescu extension theorems.

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