A simple example of a normal operator on a Banach space such that

Authors:
Muneo Chō and Hiroyasu Yamaguchi

Journal:
Proc. Amer. Math. Soc. **108** (1990), 143

MSC:
Primary 47B15; Secondary 15A60, 47A10

MathSciNet review:
990417

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Abstract: Bonsall and Duncan's book ([1, Theorem 25.6]) exhibits a normal element of a Banach algebra such that . In this paper, we will give a simpler example of a normal operator on a Banach space such that .

**[1]**F. F. Bonsall and J. Duncan,*Numerical ranges. II*, Cambridge University Press, New York-London, 1973. London Mathematical Society Lecture Notes Series, No. 10. MR**0442682****[2]**J. Kyle,*Numerical ranges of derivations*, Proc. Edinburgh Math. Soc. (2)**21**(1978/79), no. 1, 33–39. MR**0487502****[3]**Marvin Rosenblum,*On the operator equation 𝐵𝑋-𝑋𝐴=𝑄*, Duke Math. J.**23**(1956), 263–269. MR**0079235****[4]**Joseph G. Stampfli,*The norm of a derivation*, Pacific J. Math.**33**(1970), 737–747. MR**0265952**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0990417-2

Keywords:
Banach space,
normal operator,
operator norm,
spectral radius

Article copyright:
© Copyright 1990
American Mathematical Society