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The Minimum Numbers for Certain Positive Operators

Ching-Yun Suen

Journal of Mathematics Research, 2020, vol. 12, issue 5, 15

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) .

JEL-codes: R00 Z0 (search for similar items in EconPapers)
Date: 2020
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Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:5:p:15