Journal of Operator Theory

Volume 68, Issue 1, Summer 2012 pp. 173-178.

Stinespring's theorem for maps on Hilbert $C^*$-modules

Authors: B.V. Rajarama Bhat (1), G. Ramesh (2), and K. Sumesh (3)
Author institution: (1) Statistical Mathematics Unit, ISI Bangalore, 560 059, India
(2) Statistical Mathematics Unit, ISI Bangalore, 560 059, India
(3) Statistical Mathematics Unit, ISI Bangalore, 560 059, India

Summary: We strengthen Mohammad B. Asadi's analogue of Stinespring's theorem for certain maps on Hilbert $C^*$-modules. We also show that any two minimal Stinespring representations are unitarily equivalent. We illustrate the main theorem with an example.

Keywords: $C^*$-algebra, completely positive map, Stinespring representation, Hilbert $C\sp{\ast}$-module

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