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 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |