6 papers
Complexity Rank of AT Algebras of Real Rank Zero
Qingnan An, Kang Li, Zhichao Liu
In this paper, we prove that every separable unital AT algebra of real rank zero has complexity rank at most one. In particular, every irrational rotation algebra has complexity ra…
Integral operators in the spaces of functions of bounded Schramm variation
Jacek Gulgowski, Piotr Kasprzak, Piotr Maćkowiak
In this paper we provide a full characterization of linear integral operators acting from the space of functions of bounded Jordan variation to the space of functions of bounded Sc…
Properties of local orthonormal systems, Part II: Geometric characterization of Bernstein inequalities
Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
Let be a probability space and let be a binary filtration, i.e. exactly one atom of is divided into two atoms of $\m…
Properties of local orthonormal systems, Part I: Unconditionality in
Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
Assume that we are given a filtration on a probability space of the form that each is generated by the partition of one a…
Compactness in Lipschitz spaces and around
Jacek Gulgowski, Piotr Kasprzak, Piotr Maćkowiak
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/Hölder continuous mappings acting from a compact metric space to a normed space. To this end som…
Compactness in normed spaces: a unified approach through semi-norms
Jacek Gulgowski, Piotr Kasprzak, Piotr Maćkowiak
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms…