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On the norm and numerical radius of Hermitian elements

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References

  1. N. I. Akhiezer,Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  2. J.-P. Kahane,Séries de Fourier Absolument Convergentes, Springer-Verlag, Berlin-Heidelberg-New York (1970).

    Google Scholar 

  3. V. E. Katsnelson, The norm of a conservative operator is equal to its spectral radius,Mat. Issled. (Kishinev),5, 3, 186–189 (1970).

    MATH  Google Scholar 

  4. M. G. Krein, On representation of functions by Fourier-Stieltjes integrals,Uch. Zapiski Kuibyshevskogo Ped. Inst.,7, 123–147 (1943).

    Google Scholar 

  5. B. Ya. Levin,Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence (1964, 1980).

    Google Scholar 

  6. R. P. Boas and A. C. Schaeffer, Variational methods in entire functions,Amer. J. Math.,79, 857–884 (1957).

    MathSciNet  Google Scholar 

  7. F. F. Bonsall and M. J. Crabb, The spectral radius of Hermitian elements of a Banach algebra,Bull. London Math. Soc.,2, 178–180 (1970).

    MathSciNet  Google Scholar 

  8. F. F. Bonsall and J. Duncan,Numerical Ranges, Cambridge Univ. Press, Cambridge (London Math. Soc. Lecture Notes Series, 2) (1971).

    Google Scholar 

  9. A. Browder, On the Bernstein inequality and the norm of Hermitian operators,Amer. Math. Monthly,78, 871–873 (1971).

    MATH  MathSciNet  Google Scholar 

  10. M. J. Crabb and M. C. McGregor, Polynomials in a Hermitian element,Glasgow Math. J.,30, 171–176 (1988).

    MathSciNet  Google Scholar 

  11. E. A. Gorin, Bernstein's inequality from the point of view of operator theory,Selecta Math. Sovietica,7, 191–219 (1988).

    MATH  Google Scholar 

  12. A. M. Sinclair, The Banach algebra generated by a Hermitian operator,Proc. London Math. Soc., 3,24, 681–691 (1972).

    MATH  MathSciNet  Google Scholar 

  13. I. Vidav, Eine metrische Kennzeichnung der selbstadjungierten Operatoren,Math. Z.,66, 121–128 (1956).

    Article  MATH  MathSciNet  Google Scholar 

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Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 2, pp. 248–254, April–June, 1994.

Translated by V. Mackevičius

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Norvidas, S. On the norm and numerical radius of Hermitian elements. Lith Math J 34, 201–204 (1994). https://doi.org/10.1007/BF02333417

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  • DOI: https://doi.org/10.1007/BF02333417

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