Non-Bounded Operators

  • K. O. Friedrichs
Part of the Applied Mathematical Sciences book series (AMS, volume 9)

Abstract

Operators which are not bounded will not be defined in the whole Hilbert space ℌ, but only in a subspace of b , called the “domain” of the operator and denoted by b A. Operators defined only in a subspace of b occur quite frequently. Of course, integral operators are naturally defined only in such subspaces of b. But if they are bounded — and those that we have considered are bounded — they can be extended to the whole space ℌ. Differential operators also are defined only in subspaces — as was already indicated in Chapter I; but they are always strictly non-bounded, as will be shown in Chapter VII. Of course one will naturally try to extend the domain of a non-bounded operator as far as possible.

Keywords

Hilbert Space Functional Calculus Extension Theorem Selfadjoint Operator Piecewise Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1973

Authors and Affiliations

  • K. O. Friedrichs
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA

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