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July 2019 Positivity of 2×2 block matrices of operators
Mohammad Sal Moslehian, Mohsen Kian, Qingxiang Xu
Banach J. Math. Anal. 13(3): 726-743 (July 2019). DOI: 10.1215/17358787-2019-0019

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 2×2 block matrices of operators on Hilbert spaces. Finally, we describe the nature of such block matrices and provide several ways for showing their positivity.

Citation

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Mohammad Sal Moslehian. Mohsen Kian. Qingxiang Xu. "Positivity of 2×2 block matrices of operators." Banach J. Math. Anal. 13 (3) 726 - 743, July 2019. https://doi.org/10.1215/17358787-2019-0019

Information

Received: 12 March 2019; Accepted: 27 March 2019; Published: July 2019
First available in Project Euclid: 18 May 2019

zbMATH: 07083769
MathSciNet: MR3978945
Digital Object Identifier: 10.1215/17358787-2019-0019

Subjects:
Primary: 47A63
Secondary: 46L05

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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