Concerning the Cesàro matrix and its immediate offspring

H. C. Rhaly Jr.

Received: November 17, 2013;   Accepted: January 15, 2014

Abstract.   For the Cesàro matrix C in B(l2)$ and the unilateral shift U, it is known that C and its immediate offspring U*CU are both hyponormal and noncompact, and they have the same norm and the same spectrum. Here we investigate similarity and unitary equivalence for C and U*CU, as well as further generations of offspring.
Necessary conditions are found for a lower triangular factorable matrix to be unitarily equivalent to its immediate offspring. A specialized result is obtained for factorable matrices having a constant main diagonal. Along the way, a more general result is also obtained: necessary conditions are found for two lower triangular factorable matrices to be unitarily equivalent.

Keywords:  Cesàro matrix; factorable matrix, similarity; unitary equivalence.  

AMS Subject classification: Primary:  47B99  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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