Extensions of bitriangular operators
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We prove that every one-dimensional extension of a bitriangular operator has a cyclic commutant. We also prove that if T is an extension of a bitriangular operator by an algebraic operator, then the weakly closed algebra W(T) generated by T has a separating vector.
INTEGRAL EQUATIONS AND OPERATOR THEORY
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Larson, D. R., & Wogen, W. R.
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