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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalizations of certain nest algebra results


Author: N. K. Spanoudakis
Journal: Proc. Amer. Math. Soc. 115 (1992), 711-723
MSC: Primary 47D30
DOI: https://doi.org/10.1090/S0002-9939-1992-1097353-6
MathSciNet review: 1097353
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Abstract: In this paper we discuss generalizations from the Hilbert space case to more general settings of certain theorems concerning a nest algebra $ \mathcal{L}$, namely, (a) the solvability of $ Tx = y$ within $ \operatorname{Alg} \mathcal{L}$, (b) the decomposability of finite rank operators of $ \operatorname{Alg} \mathcal{L}$ by rank one such operators, and (c) approximability in the strong operator topology of $ \operatorname{Alg} \mathcal{L}$ by its finite ranks.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1097353-6
Keywords: Nest, nest algebra, finite rank, interpolation, approximation
Article copyright: © Copyright 1992 American Mathematical Society