A simple example of a normal operator $T$ on a Banach space such that $r(T)<\Vert T\Vert$
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- by Muneo ChΕ and Hiroyasu Yamaguchi
- Proc. Amer. Math. Soc. 108 (1990), 143
- DOI: https://doi.org/10.1090/S0002-9939-1990-0990417-2
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Abstract:
Bonsall and Duncanβs book ([1, Theorem 25.6]) exhibits a normal element $h + ik$ of a Banach algebra such that $r(h + ik) < ||h + ik||$. In this paper, we will give a simpler example of a normal operator $T$ on a Banach space such that $r(T) < ||T||$.References
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- J. Kyle, Numerical ranges of derivations, Proc. Edinburgh Math. Soc. (2) 21 (1978/79), no.Β 1, 33β39. MR 487502, DOI 10.1017/S0013091500015856
- Marvin Rosenblum, On the operator equation $BX-XA=Q$, Duke Math. J. 23 (1956), 263β269. MR 79235
- Joseph G. Stampfli, The norm of a derivation, Pacific J. Math. 33 (1970), 737β747. MR 265952
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 143
- MSC: Primary 47B15; Secondary 15A60, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1990-0990417-2
- MathSciNet review: 990417