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## 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.

#### Authors

• Albert Jeu-Liang SheuDepartment of Mathematics
University of Kansas
Lawrence, KS 66045, U.S.A.
ORCID: 0000-0001-5613-0240
e-mail
• Thomas TimmermannFB Mathematik und Informatik
University of Münster
Münster, Germany
e-mail

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