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6 papers
A note on disjointness and discrete elements in partially ordered vector spaces
Jani Jokela
The notions of disjointness and discrete elements play a prominent role in the classical theory of vector lattices. There are at least three different generalizations of the notion…
Partially ordered semigroups and groups with two mixed partial orderings
Jani Jokela
A mixed lattice is a partially ordered set with two mixed partial orderings that are linked by asymmetric upper and lower envelopes. These notions generalize the join and meet oper…
General mixed lattices
Jani Jokela
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studi…
Mixed lattice structures and cone projections
Jani Jokela
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have be…
Compatible topologies on mixed lattice vector spaces
Jani Jokela
A mixed lattice vector space is a partially ordered vector space with two partial orderings, generalizing the notion of a Riesz space. Whereas the algebraic theory of mixed lattice…
Ideals, bands and direct sum decompositions in mixed lattice vector spaces
Jani Jokela
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental result…