Heredity for triangular operators
Keywords:
posinormal operator, dominant operator, compact operator, $M$-hyponormal operator, hyponormal operator, triangular matrix, terraced matrix
Abstract
A proof is given that if the lower triangular infinite matrix $T$ acts boundedly on $\ell^2$ and U is the unilateral shift, the sequence $(U^*)^nTU^n$ inherits from $T$ the following properties: posinormality, dominance, $M$-hyponormality, hyponormality, normality, compactness, and noncompactness. Also, it is demonstrated that the upper triangular matrix $T^*$ is dominant if and only if $T$ is a diagonal matrix.Downloads
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Published
2013-12-12
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