A note on the quantum family of maps
Volume 120 / 2020
Banach Center Publications 120 (2020), 111-120
MSC: 46L85.
DOI: 10.4064/bc120-8
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 $C(X)$ 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.
