Posinormal terraced matrices
Bull. Korean Math. Soc. 2009 Vol. 46, No. 1, 117-123
Printed January 1, 2009
H. Crawford Rhaly, Jr.
1081 Buckley Drive, Jackson, Mississippi 39206, U.S.A
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 $\ell^2$; 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 $MM$*=$M$*$PM$ for some positive operator $P$ on $\ell^2$; these conditions lead to new sufficient conditions for the hyponormality of $M$. Sufficient conditions are also found for the adjoint $M$* to be posinormal, and it is observed that, unless $M$ is essentially trivial, $M$* cannot be hyponormal. A few examples are considered that exhibit special behavior.
Keywords : Ces\`{a}ro matrix, terraced matrix, dominant operator, hyponormal operator, posinormal operator
MSC numbers : Primary 47B99
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