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Interpolation problems for ideals in nest algebras

Published online by Cambridge University Press:  24 October 2008

M. Anoussis ,
E. G. Katsoulis ,
R. L. Moore  and
T. T. Trent
M. Anoussis
Affiliation:
Department of Mathematics, Aegean University, Karlovasi 83200, Greece
E. G. Katsoulis
Affiliation:
Department of Mathematics, Lancaster University, Lancaster LA1 4YF
R. L. Moore
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.
T. T. Trent
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.
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Abstract

Given 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 151 - 160
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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