Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are {\em{two}} types of irreducible tensor operator, which may be called `ordinary' and `twisted'. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner-Eckart theorem for both the ordinary and twisted operators. Examples of irreducible tensor operators for the standard deformation of the function algebra of the compact Lie group $SU(2)$ are described to demonstrate the applicability of the new definitions.