Abstract
We prove that it is possible for two uniform algebras to have the same scalar interpolating sets, yet still have different matrix-valued interpolating sets.
We prove a result for tensor products of uniform algebras that extends Agler's interpolation formula for the bidisk to more general product domains. This is accomplished by introducing a dual object for interpolation problems, which we call a Schur ideal, and proving that the Schur ideal for a tensor product is the intersection of the corresponding Schur ideals.
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Research supported in part by a grant from the NSF
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Paulsen, V.I. Matrix-valued interpolation and hyperconvex sets. Integr equ oper theory 41, 38–62 (2001). https://doi.org/10.1007/BF01202530
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DOI: https://doi.org/10.1007/BF01202530