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.
- Full Text: PDF
- DOI:10.5539/jmr.v10n6p30
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