Natural closures, natural compositions and natural sums of monotone operators
The author presents the natural topology \(\nu\) on the product \(X\times X^*\) of a Banach space with its dual space, and studies the properties of monotone operators in this topology. Then he defines the following generalized operations: the natural / fuzzy / natural extended / natural variational composition of an operator \(M:Y\rightrightarrows Y^*\) with a linear operator \(A:X\to Y\), and the natural / fuzzy sum of two operators \(M,\,N:X\rightrightarrows X^*\), where \(X,\,Y\) are Banach spaces. Their properties (pointing out the case of monotone operators) and connections between them and other notions or previous constructions by Attouch-Baillon-Théra, Revalski-Théra and Pennanen-Revalski-Théra are investigated in this paper.
scientific article; zbMATH DE number 5292200
scientific article