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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invertibility in nest algebras


Authors: Avraham Feintuch and Alan Lambert
Journal: Proc. Amer. Math. Soc. 91 (1984), 573-576
MSC: Primary 47C05; Secondary 47A05
MathSciNet review: 746092
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Abstract: Let $ \mathcal{F}$ denote a complete nest of subspaces of a complex Hilbert space $ \mathcal{H}$, and let $ \mathcal{C}$ denote the nest algebra defined by $ \mathcal{F}$. Let $ \mathcal{K}$ denote the ideal of compact operators on $ \mathcal{H}$. If $ \mathcal{F}$ has no infinite-dimensional gaps then $ T \in \mathcal{C}$ is invertible in $ \mathcal{C}$ if and only if it is invertible in $ \mathcal{C} + \mathcal{K}$. An example is given of a nest with an infinite gap for which there exists an operator in $ \mathcal{C}$ which is invertible in $ \mathcal{C} + \mathcal{K}$ but not in $ \mathcal{C}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746092-2
PII: S 0002-9939(1984)0746092-2
Article copyright: © Copyright 1984 American Mathematical Society