Uniformly bounded composition operators between general Lipschitz function normed spaces

Janusz Matkowski

Abstract


The notions of uniform boundedness and equidistant uniform boundedness of an
operator (both weaker then usual boundedness) are introduced. The main
results say that the generator of any uniformly bounded (or equidistantly
uniformly bounded) composition Nemytskiń≠ operator acting between general
Lipschitzian normed function spaces must be affine with respect to the
function variable.

Keywords


Composition operator; uniformly bounded operator; Lipschitz function normed space

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