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Proceedings of the American Mathematical Society

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

 

 

On bi-quasitriangular operators


Author: L. J. Gray
Journal: Proc. Amer. Math. Soc. 64 (1977), 291-294
MSC: Primary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1977-0454698-X
MathSciNet review: 0454698
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Abstract: It is shown that the set of nilpotent operators T for which $ {T^k}$ has closed range for all k is norm dense in the set of all nilpotent operators. A consequence of this is that every bi-quasitriangular operator is a norm limit of operators which are similar to a direct sum of weighted shifts plus scalars.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0454698-X
Keywords: Bi-quasitriangular, nilpotent operator, algebraic operator, closed range
Article copyright: © Copyright 1977 American Mathematical Society