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arXiv · 1811.05744

A note on weak positive matrices, finite mass measures and hyponormal weighted shifts

H. El Azhar·K. Idrissi·E. H. Zerouali
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Abstract

We study the class of Hankel matrices for which the $k\times k$-block-matrices are positive semi-definite. We prove that a $k\times k$-block-matrix has non zero determinant if and only if all $k\times k$-block matrices have non zero determinant. We use this result to extend the notion of propagation phenomena to $k$-hyponormal weighted shifts. Finally we give a study on invariance of $k$-hyponormal weighted shifts under one rank perturbation.

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H. El Azhar, K. Idrissi, E. H. Zerouali. 2018-11-14. A note on weak positive matrices, finite mass measures and hyponormal weighted shifts. https://doi.org/10.13108/2019-11-3-88

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