Maximal noncompactness of embeddings into Marcinkiewicz spaces

Jan Malý, Zdeněk Mihula, Vít Musil, Luboš Pick

Published 2024-04-06Version 1

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can be derived that such operators are almost always maximally noncompact in the sense that their ball measure of noncompactness coincides with their operator norm. We point out specifications of the universal principle to the case of the identity operator.