Positivity of $2\times 2$ block matrices of operators

By Mohammad Sal Moslehian, M. Kian, Qingxiang Xu. Banach Journal of Mathematical Analysis, 2019

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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 $2\times 2$ block matrices of operators in Hilbert spaces and finally describe the nature of such block matrices and provide several ways for showing their positivity.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bccdbe2a3f6f6f0defadae234dd9c9ae89bb98a5