POSINORMAL TERRACED MATRICES

Title & Authors
POSINORMAL TERRACED MATRICES
Rhaly, H. Crawford, Jr.;

Abstract
This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on $\small{{\ell}^2}$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $\small{MM^*=M^*PM}$ for some positive operator P on $\small{{\ell}^2}$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $\small{M^*}$ to be posinormal, and it is observed that, unless M is essentially trivial, $\small{M^*}$ cannot be hyponormal. A few examples are considered that exhibit special behavior.
Keywords
$\small{Ces{\grave{a}}ro}$ matrix;terraced matrix;dominant operator;hyponormal operator;posinormal operator;
Language
English
Cited by
1.
REMARKS CONCERNING SOME GENERALIZED CES$\grave{A}$RO OPERATORS ON ${\ell}^2$,;

충청수학회지, 2010. vol.23. 3, pp.425-434
References
1.
A. Brown, P. R. Halmos, and A. L. Shields, Cesaro operators, Acta Sci. Math. (Szeged) 26 (1965), 125–137.

2.
G. Hardy, J. E. Littlewood, and G. P´olya, Inequalities, Second Edition, Cambridge University Press, Cambridge, 1989.

3.
C. S. Kubrusly and B. P. Duggal, On posinormal operators, Adv. Math. Sci. Appl. 17 (2007), no. 1, 131–147.

4.
G. Leibowitz, Rhaly matrices, J. Math. Anal. Appl. 128 (1987), no. 1, 272–286.

5.
H. C. Rhaly, Jr., p-Cesaro matrices, Houston J. Math. 15 (1989), no. 1, 137–146.

6.
H. C. Rhaly, Jr., Terraced matrices, Bull. London Math. Soc. 21 (1989), no. 4, 399–406.

7.
H. C. Rhaly, Jr., Posinormal operators, J. Math. Soc. Japan 46 (1994), no. 4, 587–605.

8.
H. C. Rhaly, Jr., Hyponormal terraced matrices, Far East J. Math. Sci. 5 (1997), no. 3, 425–428.

9.
H. C. Rhaly, Jr., A note on heredity for terraced matrices, Gen. Math. 16 (2008), no. 1, 5–9.

10.
J. G. Stampfli and B. L. Wadhwa, On dominant operators, Monatsh. Math. 84 (1977), no. 2, 143–153.