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) .

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