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Journal of Operator Theory

Volume 50, Issue 2, Fall 2003  pp. 249-261.

An intrinsic difficulty with interpolation on the bidisk

Authors James P. Solazzo
Author institution: Department of Mathematics, University of Georgia, Athens, GA 30602, USA

Summary:  The set of possible values (w1,,wk)=(f(x1),,f(xk)) arising from restricting contractive elements f from some uniform algebra A to a finite set {x1,,xk} in the domain is called an interpolation body. When the uniform algebra is the bidisk algebra, Cole and Wermer show that the associated interpolation body is a semi-algebraic set and it is in this sense that the interpolation body is ``computable''. Motivated by the work of Cole and Wermer, Paulsen introduced the notion of the Schur ideal which acts a natural ``dual'' object for these interpolation bodies. From this ``duality'' a stronger notion of ``computability'' follows which will allow us to discuss the intrinsic differences between interpolation on the bidisk and interpolation on the disk.


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