Title : ( Positivity of $2\times 2$ block matrices of operators )
Authors: Mohsen Kian , Qingxiang Xu ,
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Abstract
We review some significant generalizations and applications of the celebrated Douglas theorem on 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 on Hilbert spaces and finally describe the nature of such block matrices and provide several ways for showing their positivity.
Keywords
, positive operator, block matrix, Hilbert space
@article{paperid:1074330,
author = {Mohsen Kian and Qingxiang Xu},
title = {Positivity of $2\times 2$ block matrices of operators},
journal = {Banach Journal of Mathematical Analysis},
year = {2019},
volume = {13},
number = {3},
month = {July},
issn = {1735-8787},
pages = {726--743},
numpages = {17},
keywords = {positive operator; block matrix; Hilbert space},
}
%0 Journal Article
%T Positivity of $2\times 2$ block matrices of operators
%A Mohsen Kian
%A Qingxiang Xu
%J Banach Journal of Mathematical Analysis
%@ 1735-8787
%D 2019
