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

 

Counterexamples concerning bitriangular operators


Authors: M. S. Lambrou and W. E. Longstaff
Journal: Proc. Amer. Math. Soc. 112 (1991), 783-787
MSC: Primary 47A66; Secondary 47A15, 47A65, 47D25
MathSciNet review: 1052576
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Abstract: An operator on a separable Hilbert space is called bitriangular if it and its adjoint have upper triangular representations with respect to two (perhaps different) orthonormal bases. Although bitriangular operators have some tractable properties and seem to be the right context for generalization of matrices to infinite dimensions, we give counterexamples to various open problems regarding this class of operators. The counterexamples make use of a property that an $ M$-basis may or may not have.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1052576-6
PII: S 0002-9939(1991)1052576-6
Keywords: Triangular operator, bitriangular operator, invariant subspace, $ M$-basis, strong $ M$-basis
Article copyright: © Copyright 1991 American Mathematical Society