Geodesic
Concerning the Cesaro matrix and its immediate offspring
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 27-38 
Crawford Rhaly; Crawford Rhaly. Concerning the Cesaro matrix and its immediate offspring. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a2/
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     author = {Crawford Rhaly and Crawford Rhaly},
     title = { Concerning the {Cesaro} matrix and its immediate offspring},
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     pages = {27--38},
     year = {2015},
     volume = {84},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a2/}
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For the Cesaro matrix C 2 B(l2) and the unilateral shift U, it is known that C and its immediate ospring UCU are both hyponormal and noncompact, and they have the same norm and the same spectrum. Here we investigate similarityand unitary equivalence for C and U*CU, as well as further generations of ospring.Necessary conditions are found for a lower triangular factorable matrix to be unitarily equivalent to its immediate ospring. A specialized result is obtained for factorable matrices having a constant main diagonal. Along the way, a more generalresult is also obtained: necessary conditions are found for two lower triangular factorable matrices to be unitarily equivalent.