9 citations · 15 across the 10 of their papers we have counts for
13 papers
The -strong duals of and
Florian Boisen, Anke Kalauch, Wen-Chi Kuo +2
For a conditional expectation operator on a Dedekind complete Riesz space, we give representations of the -strong duals of and . The representation for…
A functional representation approach to vector lattice covers for spaces of compact operators
Onno van Gaans, Jochen Glück, Anke Kalauch
For ordered normed vector spaces , we consider the space of bounded linear operators and characterize when its cone of positive operators has non-empty int…
Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres
Onno van Gaans, Anke Kalauch, Mark Roelands
Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison's anti-lattice theorem, we show that each of these factors is a disjointnes…
Strong completeness of a class of L2-type Riesz spaces
Anke Kalauch, Wenchi Kuo, Bruce Watson
Strong convergence and convergence in probability were generalized to the setting of a Riesz space with conditional expectation operator, T, in [Y. Azouzi, W.-C. Kuo, K. Ramdane, B…
A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces
Anke Kalauch, Wen-Chi Kuo, Bruce Alastair Watson
We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [{{\sc B. A. Watson}, {An Andô-Douglas type theorem in Riesz spaces with a conditional expectation,} {…
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…
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…
Order continuity from a topological perspective
Till Hauser, Anke Kalauch
We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spa…
Disjointness preserving -semigroups and local operators on ordered Banach spaces
Anke Kalauch, Onno van Gaans, Feng Zhang
We generalize results concerning -semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving $\math…
Bands in partially ordered vector spaces with order unit
Anke Kalauch, Bas Lemmens, Onno van Gaans
In an Archimedean directed partially ordered vector space one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover $Y…
A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term
Anke Kalauch, Rainer Picard, Stefan Siegmund +2
We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we…