# The Weighted Mean Operator on l2 with the Weight Sequence w n=n1 is Hyponormal

### From NZJM

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**New Zealand Journal of Mathematics**

**Vol.** 44, (2014), **Pages** 103-106

**H. C. Rhaly Jr.**

1081 Buckley Drive,

Jackson, MS 39206, U.S.A.

**B. E. Rhoades**

Indiana University,

Department of Mathematics,

Bloomington, IN 47405, U.S.A.

**Abstract** Posinormality is used to demonstrate that the weighted mean matrix whose weight sequence is the sequence of positive integers is a hyponormal operator on *l*^{2}.

**Keywords** Posinormal operator, hyponormal operator, factorable matrix, weighted mean matrix.

**Classification** (MSC2000) Primary 47B99.

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