The weighted mean matrix with weight sequence $w_n=2n+1$ is a hyponormal operator on $\ell^2$

H. C. Rhaly

The weighted mean matrix with weight sequence $w_n=2n+1$ is a hyponormal operator on $\ell^2$

Functional Analysis 2019-01-18 v6

Authors: H. C. Rhaly

Abstract

A weighted mean matrix whose weight sequence is linear with positive coefficients is shown to be a posinormal operator on $\ell^2$ . This operator is also shown to be coposinormal, so it and its adjoint have the same null space and the same range. The posinormality result leads to a proof that the weighted mean matrix associated with the sequence of odd positive integers is hyponormal, as well as a conjecture regarding a more general linear case.

Keywords

weighted mean matrix hyponormal operator posinormal operator coposinormal operator weight sequence adjoint operator null space range

Cite

@article{arxiv.1409.5156,
  title  = {The weighted mean matrix with weight sequence $w_n=2n+1$ is a hyponormal operator on $\ell^2$},
  author = {H. C. Rhaly},
  journal= {arXiv preprint arXiv:1409.5156},
  year   = {2019}
}

Comments

9 pages; conjecture revised

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