Abstract
This paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the [Formula: see text]-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified. Then these representations are realized by multiplication operators on an [Formula: see text]-space. The C*-algebra of continuous functions vanishing at infinity is defined by considering an *-algebra such that its classical counterpart separates the points of the [Formula: see text]-dimensional complex space and by taking the operator norm closure of a universal representation of this algebra.
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