9 citations · 26 across the 4 of their papers we have counts for
6 papers
Projection bands and atoms in pervasive pre-Riesz spaces
Anke Kalauch, Helena Malinowski
In vector lattices, the concept of a projection band is a basic tool. We deal with projection bands in the more general setting of an Archimedean pre-Riesz space . We relate the…
Pervasive and weakly pervasive pre-Riesz spaces
Anke Kalauch, Helena Malinowski
Pervasive pre-Riesz spaces are defined by means of vector lattice covers. To avoid the computation of a vector lattice cover, we give two distinct intrinsic characterizations of pe…
Order continuous operators on pre-Riesz spaces and embeddings
Helena Malinowski, Anke Kalauch
We investigate properties of order continuous operators on pre-Riesz spaces with respect to the embedding of the range space into a vector lattice cover or, in particular, into its…
Order closed ideals in pre-Riesz spaces and their relationship to bands
Helena Malinowski
In Archimedean vector lattices bands can be introduced via three different coinciding notions. First, they are order closed ideals. Second, they are precisely those ideals which eq…
On finite elements in -algebras and in product algebras
Helena Malinowski, Martin R. Weber
Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in -algebras, preferably in -algebras, and in product algebras. The…
Vector lattice covers of ideals and bands in pre-Riesz spaces
Anke Kalauch, Helena Malinowski
Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover for a p…