Strict Positivity of Operators and Inflated Schur Products


  •  Ching-Yun Suen    

Abstract

In this paper we provide a characterization of strictly positive matrices of operators and a factorization of their inverses. Consequently, we provide a test of strict positivity of matrices in . We give equivalent conditions for the inequality . 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.



This work is licensed under a Creative Commons Attribution 4.0 License.