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MR990417 (90d:47024) 47B15 (15A60 47A10) Chō, Muneo; Yamaguchi, Hiroyasu A simple example of a normal operator $T$$T$ on a Banach space such that $r(T)<\Vert T\Vert $$r(T)<\Vert T\Vert$. Proc. Amer. Math. Soc. 108 (1990), no. 1, 143.

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