Abstract
In this paper, we extend a method of Arveson (J Funct Anal 20(3):208–233, 1975) and McCullough (J Funct Anal 135(1):93–131, 1996) to prove a tangential interpolation theorem for subalgebras of H ∞. This tangential interpolation result implies a Töplitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729–738, 2009) and Douglas and Sarkar (Proc CRM, 2009).
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M. Raghupathi was supported in part by a National Science Foundation Young Investigator Award, Workshop in Analysis and Probability, Texas A&M University.
B. D. Wick was supported by National Science Foundation CAREER Award DMS 0955432 and an Alexander von Humboldt Fellowship.
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Raghupathi, M., Wick, B.D. Duality, Tangential Interpolation, and Töplitz Corona Problems. Integr. Equ. Oper. Theory 68, 337–355 (2010). https://doi.org/10.1007/s00020-010-1802-y
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DOI: https://doi.org/10.1007/s00020-010-1802-y