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Full-Text Articles in Physical Sciences and Mathematics
The Von Neumann Inequality For 3 × 3 Matrices, Greg Knese
The Von Neumann Inequality For 3 × 3 Matrices, Greg Knese
Mathematics Faculty Publications
This note details how recent work of Kosiński on the three point Pick interpolation problem on the polydisc can be used to prove the von Neumann inequality for d-tuples of commuting 3 x 3 contractive matrices.
Canonical Agler Decompositions And Transfer Function Realizations, Kelly Bickel, Greg Knese
Canonical Agler Decompositions And Transfer Function Realizations, Kelly Bickel, Greg Knese
Mathematics Faculty Publications
A seminal result of Agler proves that the natural de Branges-Rovnyak kernel function associated to a bounded analytic function on the bidisk can be decomposed into two shift-invariant pieces. Agler's decomposition is non-constructive—a problem remedied by work of Ball-Sadosky-Vinnikov, which uses scattering systems to produce Agler decompositions through concrete Hilbert space geometry. This method, while constructive, so far has not revealed the rich structure shown to be present for special classes of functions--inner and rational inner functions. In this paper, we show that most of the important structure present in these special cases extends to general bounded analytic functions. We …