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 -basis may or may not have.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052576-6

Keywords:
Triangular operator,
bitriangular operator,
invariant subspace,
-basis,
strong -basis

Article copyright:
© Copyright 1991
American Mathematical Society