Resolvent and Spectrum

  • Kôsaku Yosida
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)


Let T be a linear operator whose domain D (T) and range R (T) both lie in the same complex linear topological space X. We consider the linear operator
$$ {T_\lambda } = \lambda I - T,$$
where λ is a complex number and I the identity operator. The distribution of the values of λ for which T λ has an inverse and the properties of the inverse when it exists, are called the spectral theory for the operator T. We shall thus discuss the general theory of the inverse of T λ .


Linear Operator Periodic Function Continuous Linear Operator Operational Calculus Linear Topological Space 
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Comments and References

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    Phillips, R. S. The adjoint semi-group. Pacific J. Math. 5, 269–283 (1955).MATHGoogle Scholar
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    Nagumo, M. Einige analytische Untersuchungen in linearen metrischen Ringen. Jap. J. Math. 13, 61–80 (1936).Google Scholar
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    Taylor, A. Introduction to Functional Analysis, Wiley 1958.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1968

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Department of MathematicsUniversity of TokyoTokyoJapan

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