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Operators with memory in Schramm spaces

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 3

69--80

We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.