Seminar on Functional Operators and Equations pp 102-103 | Cite as

# Operators of Locally Bounded Range

Conference paper

## 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 L, for all f e L

^{2}(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 L^{2}(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)

^{2}(a,b) and for every a ≤ x ≤ b,## Copyright information

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