Title: Notes from Operator Theory and Theory of Function spaces
Speaker: Jan Lang
Abstract: In this talk, we will explore the deep connections between Operator Theory, the Theory of Function Spaces and other areas of mathematics. Among others, our focus will be on illustrating how various classes of operators, such as compact, strictly singular, and weakly compact operators, act on spaces like Lebesgue, Lorentz, and Besov spaces. Special attention will be given to the interplay between the structural properties of these spaces—such as embeddings, duality, and interpolation—and the behavior of operators defined on them. We will also discuss recent advances in understanding the non-compactness properties of operators, particularly those arising in the context of harmonic analysis and partial differential equations. These results shed light on the subtle mechanisms that govern boundedness, compactness, and strict singularity in optimal function spaces, offering new insights into both classical and contemporary problems in analysis.
