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arXiv · 1809.11107

A Note on the Quantum Family of Maps

Albert Jeu-Liang Sheu·Thomas Timmermann
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Abstract

The notion and theory of the quantum space of all maps from a quantum space pioneered by Sołtan have been mainly focused on finite-dimensional C*-algebras which are matrix algebra bundles over a finite set $S$. We propose a modification of this notion to cover the case of $C\left( X\right) $ for general compact Hausdorff spaces $X$ instead of finite sets $S$ while taking into account of the topology of $X$. A notion of free product of copies of a unital C*-algebra topologically indexed by a compact Hausdorff space arises naturally, and satisfies some desired functoriality.

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BibTeXRIS

Albert Jeu-Liang Sheu, Thomas Timmermann. 2018-10-21. A Note on the Quantum Family of Maps. https://arxiv.org/abs/1809.11107

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