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The C*‐algebra obtained by completing the quantum group Funq(SU(2))

For positive q, the scalar product defined by the integral on Funq(SU(2)) is used to complete Funq(SU(2)) to a Hilbert space Hq. The dual map to the coproduct on Funq(SU(2)) makes Hq into a Banach algebra without unit. Multiplication from the left defines a *‐representation of Funq(SU(2)) on Hq and thus Funq(SU(2)) can be completed to a C*‐algebra Fq. This C*‐algebra is shown to coincide with the C*‐algebra SUν(2) considered by Woronowicz [Publ. RIMS, Kyoto Univ. 23, 117 (1987)]. General representations of Fq are discussed and the spectrum of Fq and its Jacobson topology are calculated.