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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 nest algebra modules


Author: Xiaoxia Zhang
Journal: Proc. Amer. Math. Soc. 130 (2002), 427-432
MSC (2000): Primary 47L35
Published electronically: May 23, 2001
MathSciNet review: 1862122
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Abstract:

Let $\mathcal{A}$ be a nest algebra and ${\mathcal L}at \mathcal{A}$ its invariant projection (or subspace) lattice. In this paper, using order homomorphisms of ${\mathcal L}at \mathcal{A}$, we give necessary and sufficient conditions on bounded linear operators $X$and $Y$ on a Hilbert space to guarantee the existence of an operator $A$ in a certain $\mathcal{A}$-module such that $AX = Y$.


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Additional Information

Xiaoxia Zhang
Affiliation: Department of Mathematics, Qufu Normal University 273165, Shan Dong, People’s Republic of China
Email: xiaoxiazhang@webpc.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06074-9
PII: S 0002-9939(01)06074-9
Keywords: Nest algebra, nest algebra module, operator interpolation, order homomorphism
Received by editor(s): March 12, 1998
Received by editor(s) in revised form: October 22, 1998, November 22, 1999, and June 14, 2000
Published electronically: May 23, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society