The Minimum Numbers for Certain Positive Operators


  •  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) .



This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

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