Darstellung von Banach-Verbänden und Sätze vom Korovkin-Typ.
Das Spektrum von Verbandsoperatoren in Banachverbänden.
Der Generator stark stetiger Verbandshalbgruppen auf C (X) und dessen Spektrum.
Determination of the Invariant Interval for Positive Linear Operators by a Nonstationary Iterative Procedure
Dilations of Positive Operators: Construction and Ergodic Theory.
Directedness in Ordered Normed Spaces and Operators.
Disjointly strictly-singular operators in Banach lattices
Disjointness preserving and diffuse operators
Dividing measures and narrow operators
We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far...
Domination of operators in the non-commutative setting
We consider majorization problems in the non-commutative setting. More specifically, suppose E and F are ordered normed spaces (not necessarily lattices), and 0 ≤ T ≤ S in B(E,F). If S belongs to a certain ideal (for instance, the ideal of compact or Dunford-Pettis operators), does it follow that T belongs to that ideal as well? We concentrate on the case when E and F are C*-algebras, preduals of von Neumann algebras, or non-commutative function spaces. In particular, we show that, for C*-algebras...