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Some extremal problems in the theory of numerical ranges. (English) Zbl 0229.46049

46H05 General theory of topological algebras
47A12 Numerical range, numerical radius
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
Full Text: DOI
[1] Beurling, A., Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionnelle.Neuvième congrès des mathématiciens Scandinaves, Helsingfors, 1938. · JFM 65.0483.02
[2] Boas, R. P.,Entire functions. Academic Press, New York, 1954. · Zbl 0058.30201
[3] Bollobás, B., The power inequality in Banach spaces.Proc. Camb. Phil. Soc. 69 (1971), 411–415. · Zbl 0216.16404
[4] – The numerical range in Banach algebras and complex functions of exponential type.Bull. London Math. Soc., 3 (1971), 27–33. · Zbl 0226.46055
[5] Bonsall, F. F., &Crabb, M. J., The spectral radius of a Hermitian element of a Banach algebra.Bull. London Math. Soc., 2 (1970), 178–180. · Zbl 0204.44304
[6] Bonsall, F. F. & Duncan, J.,Numerical ranges. London Math. Soc. Lecture Note Series, No. 2, Cambridge University Press, 1971. · Zbl 0207.44802
[7] Brown, L., Shields, A. &Zeller, K., On absolutely convergent exponential sums.Trans. Amer. Math. Soc., 96 (1960), 162–183. · Zbl 0096.05103
[8] Browder, A., States, numerical ranges, etc.,Proceeding of the Brown Informal Analysis Seminar, Summer, 1969.
[9] Crabb, M. J., Numerical range estimates for the norms of iterated operators.Glasgow Math. J., 11 (1970), 85–87. · Zbl 0244.47002
[10] Crabb, M. J. The power inequality on normed spaces.Proc. Edinb. Math. Soc., (to appear). · Zbl 0219.47004
[11] – Some results on the numerical range of an operator.J. London Math. Soc. (2), 2 (1970), 741–745. · Zbl 0201.45203
[12] Levin, B. Ja.,Distribution of zeros of entire functions. Amer. Math. Soc. Translation, Providence 1964. · Zbl 0152.06703
[13] Sinclair, A. M., The norm of a Hermitian element in a Banach algebra.Proc. Amer. Math. Soc., (to appear). · Zbl 0242.46035
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