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Strict Positivity of Operators and Inflated Schur Products

Author

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  • Ching-Yun Suen

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.

Suggested Citation

  • Ching-Yun Suen, 2018. "Strict Positivity of Operators and Inflated Schur Products," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(6), pages 30-42, December.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:30
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    Cited by:

    1. Ching-Yun Suen, 2020. "The Minimum Numbers for Certain Positive Operators," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(5), pages 1-15, December.
    2. Ching Yun Suen, 2022. "The Infimum Norm of Completely Positive Maps," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(1), pages 1-51, March.

    More about this item

    Keywords

    positive operators; strictly positive operators; strictly completely positive; inflated Schur products;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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