Disjointly homogeneous Banach lattices and applications

This is a survey on disjointly homogeneous Banach lattices and their applicactions. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers of operators allowing for a unified treatment of well-known results.Comment: 20 pages, to appear in Proceedings Positivity VII Conference (2013

Disjointly Homogeneous Banach Lattices and Applications

This is a survey on disjointly homogeneous Banach lattices and their applications. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers of operators allowing for a unified treatment of well-known results

Composition operators on Banach function spaces

The aim of this thesis is to provide a survey of the topic of composition operators on spaces of (equivalence classes of) measurable functions and attempt to unify some of the most important results contained in the literature. A large class of these spaces can be equipped with norms turning them into Banach lattices. These spaces are called Banach function spaces and examples include the Lebesgue, Lorentz, Orlicz and Orlicz-Lorentz spaces

Isometric factorization of vector measures and applications to spaces of integrable functions

Let X be a Banach space, Σ be a σ-algebra, and be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pełczyński factorization procedure that there exist a reflexive Banach space Y, a vector measure and an injective operator such that m factors as . We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pełczyński factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on is weakly compact, then is equal, up to equivalence of norms, to some where Y is reflexive; here we prove that the above equality can be taken to be isometric.publishedVersionPaid open acces