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

Santanu Dey; Harsh Trivedi

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arXiv · 1511.05755

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

Santanu Dey·Harsh Trivedi

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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.

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BibTeX RIS

Santanu Dey, Harsh Trivedi. 2015-11-18. KSGNS construction for $\tau$-maps on S-modules and $\mathfrak{K}$-families. https://arxiv.org/abs/1511.05755

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