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)
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