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Register a new userOn the Stampfli point of some operators and matrices
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The center of mass of an operator $A$ (denoted St($A$), and called in this paper as the {em Stampfli point} of A) was introduced by Stampfli in his Pacific J. Math (1970) paper as the unique $lambdainmathbb C$ delivering the minimum value of the norm of $A-lambda I$. We derive some results concerning the location of St($A$) for several classes of operators, including 2-by-2 block operator matrices with scalar diagonal blocks and 3-by-3 matrices with repeated eigenvalues. We also show that for almost normal $A$ its Stampfli point lies in the convex hull of the spectrum, which is not the case in general. Some relations between the property St($A$)=0 and Roberts orthogonality of $A$ to the identity operator are established.
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