Abstract. We show that an invertible operator $A$ is unitary if the numerical radius satisfies $w(A) \leqq 1$ and $w(A^{-1}) \leqq 1$.
AMS Subject Classification
(1991): 47A12, 47A63
Keyword(s):
numerical radius,
unitary operator,
numerical range
Received August 5, 2009, and in revised form August 28, 2009. (Registered under 93/2009.)
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