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Search: MSC category 47A57 ( Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60] )

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1. CMB 2010 (vol 54 pp. 3)

Bakonyi, M.; Timotin, D.
Extensions of Positive Definite Functions on Amenable Groups
Let $S$ be a subset of an amenable group $G$ such that $e\in S$ and $S^{-1}=S$. The main result of this paper states that if the Cayley graph of $G$ with respect to $S$ has a certain combinatorial property, then every positive definite operator-valued function on $S$ can be extended to a positive definite function on $G$. Several known extension results are obtained as corollaries. New applications are also presented.

Categories:43A35, 47A57, 20E05

2. CMB 2003 (vol 46 pp. 59)

Constantinescu, T.; Johnson, J. L.
A Note on Noncommutative Interpolation
In this paper we formulate and solve Nevanlinna-Pick and Carath\'eodory type problems for tensor algebras with data given on the $N$-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure theory.

Categories:47A57, 47A20

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