On the Operator Equations $A^n=A^*A$

Souheyb Dehimi; Mohammed Hichem Mortad; Zsigmond Tarcsay

On the Operator Equations $A^n=A^*A$

Functional Analysis 2019-02-07 v1

Authors: Souheyb Dehimi , Mohammed Hichem Mortad , Zsigmond Tarcsay

Abstract

Let $n\in\mathbb{N}$ and let $A$ be a closed linear operator (everywhere bounded or unbounded). In this paper, we study (among others) equations of the type $A^*A=A^n$ where $n\geq2$ and see when they yield $A=A^*$ (or a weaker class of operators). In case $n\geq3$ , we have in fact a new class of operators which could placed right after orthogonal projections and just before normal operators.

Keywords

operator theory numerical range operator theory and elliptic operators

Cite

@article{arxiv.1902.02193,
  title  = {On the Operator Equations $A^n=A^*A$},
  author = {Souheyb Dehimi and Mohammed Hichem Mortad and Zsigmond Tarcsay},
  journal= {arXiv preprint arXiv:1902.02193},
  year   = {2019}
}

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