manuscripta mathematica

, Volume 2, Issue 2, pp 191–202 | Cite as

Spektrum, numerischer Wertebereich und IHRE Maximumprinzipien in Banachalgebren

  • Bernd Schmidt


By a function of support a numerical range is defined for elements of complex Banach algebras. The geometric character of the definition allows to proof some results about the numerical range in a very natural way.- In the second part holomorphic perturbations of the numerical range and the spectrum are treated as perturbations of the function of support to get a maximum principle for the numerical range and the convex hull of the spectrum, whereas there is in general no maximum principle for the spectrum. This answers a question raised by A.Brown and R.G.Douglas.


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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Bernd Schmidt
    • 1
  1. 1.Mathematisches Institut der Universität65 Mainz

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