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Bhumi Amin

Publications and source records attributed to Bhumi Amin.

2 recordsLinked to original sources
arXiv2025

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

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.

math.OA↗
arXiv2025

A Radon-Nikodym theorem for CP-maps on Hilbert pro-C*-modules

We introduce an equivalence relation on the set of all completely positive maps between Hilbert modules over pro-C*-algebras and analyze the Stinespring's construction for equivalent completely positive maps. We then give a preorder relation in the collection of all completely positive maps between Hilbert modules over pro-C*-algebras and obtain a Radon-Nikodym type theorem.

math.OA↗