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 Spectral Radius Ergodic Theorem Continuous Linear Operator Operational Calculus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Gakushuin UniversityTokyoJapan

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