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%Wu
%Pei Yuan","pywu@math.nctu.edu.tw","
\section{Numerical ranges of nilpotent operators} By {Hwa-Long Gau and Pei Yuan Wu}.  

\medskip  \noindent      For any operator $A$ on a Hilbert space, let $w(A)$ and $w_{0}(A)$ denote its numerical radius and the distance from the origin to the boundary of its numerical range, respectively.  We prove that if $A$ is nilpotent with nilpotency $n$, then $w(A)$ is at most the product of $n - 1$ and $w_{0}(A)$.  When $A$ attains its numerical radius, we also determine a necessary and sufficient condition for the equality to hold.
%Numerical range, numerical radius, nilpotent operator.","47A12","15A60","","00:25:17","Sat Feb 23 2008","140.113.22.149"
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