Interpolation Problems for Schur Multipliers on the Drury-Arveson Space: from Nevanlinna-Pick to Abstract Interpolation Problem

2008 ◽  
Vol 62 (3) ◽  
pp. 301-349 ◽  
Author(s):  
Joseph A. Ball ◽  
Vladimir Bolotnikov
Keyword(s):  
Interpolation Problem ◽  
Schur Multipliers ◽  
Interpolation Problems ◽  
Arveson Space ◽  
Abstract Interpolation Problem

Interpolation problems for ideals in nest algebras

1992 ◽  
Vol 111 (1) ◽  
pp. 151-160 ◽  
Author(s):  
M. Anoussis ◽  
E. G. Katsoulis ◽  
R. L. Moore ◽  
T. T. Trent
Keyword(s):  
Hilbert Space ◽  
Interpolation Problem ◽  
Bounded Operator ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Nest Algebras ◽  
Interpolation Problems ◽  
The One ◽  
Necessary And Sufficient

AbstractGiven vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Txt = yt, for i = 1, 2,, n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases.

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