### Uniformly bounded composition operators between general Lipschitz function normed spaces

#### 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 Nemytskiĭ operator acting between general

Lipschitzian normed function spaces must be affine with respect to the

function variable.

operator (both weaker then usual boundedness) are introduced. The main

results say that the generator of any uniformly bounded (or equidistantly

uniformly bounded) composition Nemytskiĭ 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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