Completely Positive Maps: Pro-C*-algebras and Hilbert modules over Pro-C*-algebras

2024/09/29 by Bhumi Amin, Ramesh Golla, Amin, Bhumi +1 · 1 voice
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paper · pdf · doi:10.48550/arxiv.2409.19556

Abstract

In this paper, we begin by presenting a construction for induced representations of Hilbert modules over pro-C^*-algebras for a given continuous ^*-morphism between pro-C^*-algebras. Subsequently, we describe the structure of completely positive maps between two pro-C^*-algebras using Paschke's GNS construction for CP-maps on pro-C^*-algebras. Furthermore, through our construction, we establish a structure theorem for a φ-map between two Hilbert modules over pro-C^*-algebras, where φ is a continuous CP-map between pro-C^*-algebras. We also discuss the minimality of these representations.

Discussions

• arxiv.org/abs/2409.19556 [bsky, 5 points, 2 comments]

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