Hilbert C∗-modules as a subcategory of operator systems and injectivity

Hilbert C∗-modules as a subcategory of operator systems and injectivity

In this paper, we study a category whose objects are Hilbert C ∗ -modules and whose morphisms are completely semi- ϕ -maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi- ϕ -maps on Hilbert C ∗ -modules, leading to an analo...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2018-04, Vol.22 (2), p.597-607
Hauptverfasser: Asadi, Mohammad B., Behmani, Reza, Medghalchi, Ali R., Nikpey, Hamed
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Modules
Operator Theory
Potential Theory
Theorems
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container_title Positivity : an international journal devoted to the theory and applications of positivity in analysis
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creator Asadi, Mohammad B.
Behmani, Reza
Medghalchi, Ali R.
Nikpey, Hamed
description In this paper, we study a category whose objects are Hilbert C ∗ -modules and whose morphisms are completely semi- ϕ -maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi- ϕ -maps on Hilbert C ∗ -modules, leading to an analog of the Arveson’s extension theorem for completely semi- ϕ -maps (in contrast with ϕ -maps). This theorem together with previous results suggest that the completely semi- ϕ -maps are proper generalizations of the completely positive maps.
doi_str_mv 10.1007/s11117-017-0530-9
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source Business Source Complete; Springer Nature - Complete Springer Journals
subjects Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Modules
Operator Theory
Potential Theory
Theorems
title Hilbert C∗-modules as a subcategory of operator systems and injectivity
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