Compact Operators

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


Let X and Y be complex B-spaces, and let S be the unit sphere in X. An operator TL (X, Y) is said to be compact or completely continuous if the image T · S is relatively compact in Y. For a compact operator TL (X, X), the eigenvalue problem can be treated fairly completely, in the sense that the classical theory of Fredholm concerning linear integral equations may be extended to the linear functional equation Tx - λx = y with a complex parameter λ. This result is known as the Riesz-Schauder theory. F. Riesz [2] and J. Schauder [1].


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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Research Institute for Mathematical SciencesUniversity of KyotoKyotoJapan

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