Duality, Tangential Interpolation, and Toplitz Corona Problems

作者：Raghupathi Mrinal^*; Wick Brett D

来源：Integral Equations and Operator Theory, 2010, 68(3): 337-355.

DOI：10.1007/s00020-010-1802-y

• Distance formulae
• Hilbert module
• Nevanlinna-Pick interpolation
• Toeplitz corona problem

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-infinity. This tangential interpolation result implies a Toplitz 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).

• 出版日期2010-11