Geodesic
Conditions for factorable matrices to be hyponormal and dominant
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 261-265.

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Sufficient conditions are given for a lower triangular factorable matrix $M$, acting as a bounded linear operator on $\ell^2$, to be hyponormal. Necessary conditions are given for $M$ to be a dominant operator on $\ell^2$. The results are then applied to several examples, including the H-J Cesàro operators, the q-Cesàro operators and other weighted mean matrices, and some Toeplitz matrices.
Keywords: hyponormal operator, dominant operator, weighted mean matrix.
Mots-clés : factorable matrix 
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H. C. Rhaly; jr.; B. E. Rhoades. Conditions for factorable matrices to be hyponormal and dominant. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 261-265. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a33/

[1] G. Bennett, “An inequality for Hausdorff means”, Houston J. Math., 25:4 (1999), 709–744 | MR | Zbl

[2] J. Bustoz and L. F. Gordillo, “q-Hausdorff summability”, J. Comput. Anal. Appl., 7:1 (2005), 35–48 | MR | Zbl

[3] F. Hausdorff, “Summationsmethoden und momentfolgen. I”, Math Z., 9:1-2 (1921), 74–109 | DOI | MR | Zbl

[4] F. Hausdorff, “Summationsmethoden und momentfolgen. II”, Math Z., 9:3-4 (1921), 280–299 | DOI | MR | Zbl

[5] A. Jakimovski, The product of summability methods: New classes of transformations and their properties, Tech. Note (4), Contract No. AF 61(052)-187, 1959 | Zbl

[6] G. Leibowitz, “Rhaly matrices”, J. Math. Anal. Appl., 128:1 (1987), 272–286 | DOI | MR | Zbl

[7] J. M. H. Olmsted, Advanced Calculus, Appleton-Century-Crofts, New York, 1961 | Zbl

[8] H. C. Rhaly Jr., “Terraced matrices”, Bull. Lond. Math. Soc., 21:4 (1989), 399–406 | DOI | MR | Zbl

[9] H. C. Rhaly Jr., “Hyponormal terraced matrices”, Far East J. Math. Sci., 5:3 (1997), 425–428 | MR | Zbl

[10] H. C. Rhaly Jr., “Posinormal terraced matrices”, Bull. Korean Math. Soc., 46:1 (2009), 117–123 | DOI | MR | Zbl

[11] H. C. Rhaly Jr., “Remarks concerning come generalized Cesàro operators on $\ell^2$”, J. Chungcheong Math. Soc., 23:3 (2010), 425–433 | MR

[12] H. C. Rhaly Jr., “A pathological example of a dominant terraced matrix”, Bull. Math. Anal. Appl., 3:3 (2011), 9–12

[13] B. E. Rhoades, “Generalized Hausdorff matrices bounded on $\ell^p$ and $c$”, Acta Sci. Math. (Szeged), 43:3-4 (1981), 333–345 | MR | Zbl

[14] B. E. Rhoades, “The point spectra of generalized Hausdorff matrices”, J. Adv. Math. Stud., 2:1 (2009), 91–98 | MR | Zbl

[15] T. Selmanogullari, E. Savaş and B. E. Rhoades, “On $q$-Hausdorff matrices”, Taiwanese J. Math., 15:6 (2011), 2429–2437 | MR