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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Interpolation in inflated Hilbert spaces


Authors: R. L. Moore and T. T. Trent
Journal: Proc. Amer. Math. Soc. 127 (1999), 499-507
MSC (1991): Primary 47D25
MathSciNet review: 1469426
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Abstract: The interpolation problem for a reflexive algebra Alg$\mathcal{L}$ is this: Given two operators $X$ and $Y$, under what conditions can we be sure that there will exist an operator $A$ in Alg$\mathcal{L}$ such that $AX=Y$? There are simple necessary conditions that have been investigated in several earlier papers. Here we present an example to show that the conditions are not, in general, sufficient. We also suggest a strengthened set of conditions which are necessary and are ``almost'' sufficient, in the sense that they will ensure that $Y$ lies in the weak-operator closure of the set {$AX$:$A \in $Alg$\mathcal{L}$}.


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Additional Information

R. L. Moore
Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350
Email: rmoore@gp.as.ua.edu

T. T. Trent
Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04597-9
PII: S 0002-9939(99)04597-9
Received by editor(s): June 13, 1996
Received by editor(s) in revised form: May 27, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society