Proceedings of the American Mathematical Society

Author(s): Xiaoxia Zhang
Journal: Proc. Amer. Math. Soc. 130 (2002), 427-432.
MSC (2000): Primary 47L35
Posted: May 23, 2001
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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

and

on a Hilbert space to guarantee the existence of an operator

in a certain $\mathcal{A}$ -module such that

1.: Anoussis, M., Katsoulis, E. G., and Moore, R. L., Trent, T. T., Interpolation problem for ideals in certain reflexive operator algebras, Houston J. Math., 19 (1993), 63-73.
2.: Davidson, K. R., Nest algebras, Longman Scientific $\&$ Technical, 1988. MR 90f:47062
3.: Douglas, R. G., On majorization, factorization and range inclusion on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413-415. MR 34:3315
4.: Hopenwasser, A., The equation in a reflexive operator algebra, Indiana University Math. Journal, 29 (1980), 121-126. MR 81c:47014
5.: Katsoulis, E. G., Moore, R. L. and Trent, T. T., Interpolation in nest algebras and applications to operator corona theorems, J. Operator Theory, 29(1) (1993), 115-123. MR 95b:47052
6.: Knowles, G. J., On the structure of certain nest algebra modules, Can. J. Math., XXXIX, 6 (1987), 1405-1412. MR 89b:47063
7.: Lance, E. C., Some properties of Nest algebras, Proc. London Math. Soc., no.3, 19 (1969), 45-68. MR 39:3325
8.: Munch. N., Compact causal data interpolation, J. Math. Anal. Appl., no.2, 140 (1989), 407-418. MR 90c:47029

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

DOI: 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
Posted: May 23, 2001
Communicated by: David R. Larson
Copyright of article: Copyright 2001, American Mathematical Society

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