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Operators of Locally Bounded Range

  • György I. Targonski
Conference paper
Part of the Lecture Notes in Mathematics book series (volume 6)

Abstract

We conclude our discussion of Carleman operators by proving a lemma which links these to what we shall call operators of locally bounded range. Let L2 (a,b) be a Hilbert space of (real, or complex valued) functions of one real variable x, a ≤ x ≤ b. Let A be a bounded linear operator defined on L2 (a,b). We shall say that A is of locally bounded range, if a non-negative number M exists, independent of f and x, such that
$$ |\left( {Af} \right)\left( x \right)| \leqslant M|f|,{\text{ for all }}f\varepsilon {L^{2}}\left( {a,b} \right) $$
(12.1)
, for all f e L2(a,b) and for every a ≤ x ≤ b,

Copyright information

© Springer-Verlag Berlin · Heidelberg 1967

Authors and Affiliations

  • György I. Targonski
    • 1
  1. 1.Fordham UniversityUSA

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