Concerning the Cesaro matrix and its immediate offspring
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Abstract
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.
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How to Cite
Rhaly, C.
(2014).
Concerning the Cesaro matrix and its immediate offspring.
Acta Mathematica Universitatis Comenianae, 84(1), 27-38.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/28/122
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References
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2. Choi M., Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90, no. 5 (1983), 301-312.
3. Leibowitz G., Rhaly matrices, J. Math. Anal. Appl. 128 (1987), 272-286.
4. Rhaly Jr. H. C., p-Cesaro matrices, Houston Math. J. 15 (1989), no. 1, 137-146.
5. Rhaly Jr. H. C., Terraced matrices, Bull. Lond. Math. Soc. 21 (1989), 399-406.
6. Rhaly Jr. H. C., Heredity for triangular operators, Bol. Soc. Parana. Mat. (3) 31 (2013), no. 2, 231-234.
7. Rhaly Jr. H. C. and Rhoades B. E., Posinormal factorable matrices with a constant main diagonal, Rev. Un. Mat. Argentina, in press.
8. Rhoades B. E., Generalized Hausdor matrices bounded on `p and c, Acta Sci. Math. 43 (1981), no. 3-4, 333-345.