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Given a collection of test functions, one defines the associated Schur-Aglerclass as the intersection of the contractive multipliers over the collection ofall positive kernels for which each test function is a contractive multiplier.We indicate extensions of this framework to the case where the test functions,kernel functions, and Schur-Agler-class functions are allowed to be matrix- oroperator-valued. We illustrate the general theory with two examples: (1) thematrix-valued Schur class over a finitely-connected planar domain and (2) thematrix-valued version of the constrained Hardy algebra (bounded analyticfunctions on the unit disk with derivative at the origin constrained to havezero value). Emphasis is on examples where the matrix-valued version is notobtained as a simple higher-multiplicity tensoring of the scalar-valuedversion.

Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting