Abstract
In 1916 Georg Pick started the study of interpolation by bounded analytic functions in the unit disk. In 1951 John Von Neumann proved an inequality for contractions on a Hilbert space. These two subjects are in fact closely connected, as was shown by Donald Sarason in 1967. We continue the study of this relationship, from the point of view of representations of uniform algebras by operators on a Hilbert space. Our work leads us to define and investigate certain convex bodies in Cn which we call hyperconvex sets.
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Cole, B.J., Wermer, J. (1994). Pick interpolation, Von Neumann inequalities, and hyperconvex sets. In: Gauthier, P.M., Sabidussi, G. (eds) Complex Potential Theory. NATO ASI Series, vol 439. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0934-5_3
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DOI: https://doi.org/10.1007/978-94-011-0934-5_3
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