KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families

Santanu Dey; Harsh Trivedi

KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families

Operator Algebras 2018-06-12 v1 Mathematical Physics math.MP

Authors: Santanu Dey , Harsh Trivedi

Abstract

We introduce S-modules, generalizing the notion of Krein $C^*$ -modules, where a fixed unitary replaces the symmetry of Krein $C^*$ -modules. The representation theory on S-modules is explored and for a given $*$ -automorphism $\alpha$ on a $C^*$ -algebra the KSGNS construction for $\alpha$ -completely positive maps is proved. An extention of this theorem for $\tau$ -maps is also achieved, when $\tau$ is an $\alpha$ -completely positive map, along with a decomposition theorem for $\mathfrak K$ -families.

Keywords

S-modules Krein C*-modules KSGNS construction alpha-completely positive maps tau-maps representation theory decomposition theorem

Cite

@article{arxiv.1511.05755,
  title  = {KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families},
  author = {Santanu Dey and Harsh Trivedi},
  journal= {arXiv preprint arXiv:1511.05755},
  year   = {2018}
}

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17 pages

KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families

Abstract

Keywords

Cite

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