Banach Function Research Articles

Hadamard weighted geometric mean inequalities for the spectral and essential spectral radius of positive operators on Banach function and sequence spaces

We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric means of positive kernel operators on Banach function and sequence spaces. Some inequalities extend and refine known inequalities that have been established by several authors relatively recently. Several inequalities appear to be new even in the finite dimensional case.

Disjoint Hypercyclic and Disjoint Topologically Mixing Properties of Degenerate Fractional Differential Equations

The main purpose of this paper is to analyze the classes of disjoint hypercyclic and disjoint topologically mixing abstract degenerate (multi-term) fractional differential equations in Banach and Frechet function spaces. We focus special attention on the analysis of abstract degenerate differential equations of first and second order, when we also consider disjoint chaos as a linear topological dynamical property. We provide several illustrative examples and applications of our abstract results.

Compactness in Wiener amalgams on locally compact groups

We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group. Our main theorem provides a generalization of the corresponding results of Feichtinger. This paper paves the way for the study of compact multiplier operators on general Wiener amalgams on the lines of Feichtinger.