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

DOI:
https://doi.org/10.1090/S0002-9939-99-04597-9

MathSciNet review:
1469426

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Abstract | References | Similar Articles | Additional Information

Abstract: The interpolation problem for a reflexive algebra *Alg* is this: Given two operators and , under what conditions can we be sure that there will exist an operator in *Alg* such that ? 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 lies in the weak-operator closure of the set {:*Alg*}.

**1.**W. Arveson,*Interpolation Problems in Nest Algebras*, Journal of Functional Analysis**20**(1975), 208-233. MR**52:3979****2.**K. J. Harrison,*The Tensor Product Formula for Reflexive Subspace Lattices*, Canadian Mathematics Bulletin**38, number 3**(1995), 308-316. MR**96g:47042****3.**A. Hopenwasser,*The Equation in a Reflexive Operator Algebra*, Indiana University Mathematics Journal**29**(1980). MR**81c:47014****4.**E. Katsoulis, R. Moore, and T. Trent,*Interpolation in Nest Algebras and Applications to Operator Corona Theorems*, Journal of Operator Theory**29**(1993), 115-123. MR**95b:47052****5.**E. C. Lance,*Some Properties of Nest Algebras*, Proceedings of the London Mathematical Society**3, number 19**(1969), 45-68. MR**39:3325**

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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:
https://doi.org/10.1090/S0002-9939-99-04597-9

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