Strict Positivity of Operators and Inflated Schur Products

Ching-Yun Suen

Journal of Mathematics Research, 2018, vol. 10, issue 6, 30-42

Abstract: In this paper we provide a characterization of strictly positive n×n matrices of operators and a factorization of their inverses. Consequently, we provide a test of strict positivity of matrices in Mn (C) . We give equivalent conditions for the inequality I＞T *T+TT*. We prove a theorem involving inflated Schur products [4, P. 153] of positive matrices of operators with invertible elements in the main diagonal which extends the results [3, P. 479, Theorem 7.5.3 (b), (c)]. We also discuss strictly completely positive linear maps in the paper.

Keywords: positive operators; strictly positive operators; strictly completely positive; inflated Schur products (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:30

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