Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-99-04597-9
MathSciNet review: 1469426
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$}.


References [Enhancements On Off] (What's this?)

  • 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 $Tx=y$ 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D25

Retrieve articles in all journals with MSC (1991): 47D25


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

American Mathematical Society