Counterexamples concerning bitriangular operators
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- by M. S. Lambrou and W. E. Longstaff PDF
- Proc. Amer. Math. Soc. 112 (1991), 783-787 Request permission
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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- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 783-787
- MSC: Primary 47A66; Secondary 47A15, 47A65, 47D25
- DOI: https://doi.org/10.1090/S0002-9939-1991-1052576-6
- MathSciNet review: 1052576