Interpolation in inflated Hilbert spaces
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- by R. L. Moore and T. T. Trent PDF
- Proc. Amer. Math. Soc. 127 (1999), 499-507 Request permission
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 βalmostβ sufficient, in the sense that they will ensure that $Y$ lies in the weak-operator closure of the set {$AX$:$A \in$Alg$\mathcal {L}$}.References
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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
- Received by editor(s): June 13, 1996
- Received by editor(s) in revised form: May 27, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 499-507
- MSC (1991): Primary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-99-04597-9
- MathSciNet review: 1469426