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The Minimum Numbers for Certain Positive Operators

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  • Ching-Yun Suen

Abstract

In this paper we give upper and lower bounds of the infimum of k such that kI+2ReT⊗Sm is positive, where Sm is the m×m matrix whose entries are all 0’s except on the superdiagonal where they are all 1’s and T∈BH for some Hilbert space H. When T is self-adjoint, we have the minimum of k. When m=3 and T∈B(H) , we obtain the minimum of k and an inequality Involving the numerical radius w(T) .

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:5:p:15
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    References listed on IDEAS

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    1. 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.
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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