Positivity of $2\times 2$ block matrices of operators
Functional Analysis
2019-10-09 v1 Operator Algebras
Abstract
We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of operators. We then apply it to find a characterization of the positivity of block matrices of operators in Hilbert spaces and finally describe the nature of such block matrices and provide several ways for showing their positivity.
Keywords
Cite
@article{arxiv.1904.08680,
title = {Positivity of $2\times 2$ block matrices of operators},
author = {Mohammad Sal Moslehian and Mohsen Kian and Qingxiang Xu},
journal= {arXiv preprint arXiv:1904.08680},
year = {2019}
}
Comments
17 pages. This expository paper is appeared in Banach J. Math. Anal