Completely Positive Maps: Pro-C*-algebras and Hilbert modules over Pro-C*-algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912762782810112 |
|---|---|
| author | Amin, Bhumi Golla, Ramesh |
| author_facet | Amin, Bhumi Golla, Ramesh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completely Positive Maps: Pro-C*-algebras and Hilbert modules over Pro-C*-algebras Amin, Bhumi Golla, Ramesh Operator Algebras Primary: 46L05, 46L08, Secondary: 46K10 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. |
| title | Completely Positive Maps: Pro-C*-algebras and Hilbert modules over Pro-C*-algebras |
| topic | Operator Algebras Primary: 46L05, 46L08, Secondary: 46K10 |
| url | https://arxiv.org/abs/2409.19556 |