Numerical Ranges of the product of Operators

Hongke Du; Chi-Kwong Li; Kuo-Zhong Wang; Yueqing Wang; Ning Zuo

Numerical Ranges of the product of Operators

Functional Analysis 2016-09-08 v2

Authors: Hongke Du , Chi-Kwong Li , Kuo-Zhong Wang , Yueqing Wang , Ning Zuo

Abstract

We study containment regions of the numerical range of the product of operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by the spectrum of $AB$ , and conditions on $A$ and $B$ for the set equality holding are obtained. The results cover the case when $A$ and $B$ are self-adjoint operators extending the previous results on the numerical range of the product of two orthogonal projections.

Keywords

numerical range operator product line segments convex hull elliptical disks self-adjoint operators orthogonal projections

Cite

@article{arxiv.1510.01672,
  title  = {Numerical Ranges of the product of Operators},
  author = {Hongke Du and Chi-Kwong Li and Kuo-Zhong Wang and Yueqing Wang and Ning Zuo},
  journal= {arXiv preprint arXiv:1510.01672},
  year   = {2016}
}

Numerical Ranges of the product of Operators

Abstract

Keywords

Cite

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