Tensor products of Archimedean partially ordered vector spaces

@article{Gaans2010TensorPO,
  title={Tensor products of Archimedean partially ordered vector spaces},
  author={Onno van Gaans and Anke Kalauch},
  journal={Positivity},
  year={2010},
  volume={14},
  pages={705-714}
}
We study the tensor product of two directed Archimedean partially ordered vector spaces X and Y by means of Riesz completions. With the aid of the Fremlin tensor product of the Riesz completions of X and Y we show that the projective cone in X ⊗ Y is contained in an Archimedean cone. The smallest Archimedean cone containing the projective cone satisfies an appropriate universal mapping property. 
View on Springer
link.springer.com
9 Citations
Background Citations
3

9 Citations

Citation Type

Citation Type

Tensor products of function systems revisited
Based on the Archimedeanization developed by Paulsen and Tomforde, we give an explicit description for the positive cones of maximal tensor products of function systems. From this description, we…
Lexicographic Cones and the Ordered Projective Tensor Product
  • M. Wortel
  • Mathematics
    Trends in Mathematics
  • 2019
We introduce lexicographic cones, a method of assigning an ordered vector space \( \operatorname {\mathrm {Lex}}(S)\) to a poset S, generalising the standard lexicographic cone. These lexicographic…
Tensor Products of Convex Cones, Part I: Mapping Properties, Faces, and Semisimplicity
The tensor product of two ordered vector spaces can be ordered in more than one way, just as the tensor product of normed spaces can be normed in multiple ways. Two natural orderings have received…
The Extremal Structure of Convex Sets of Multilinear Operators
In an article published forty years ago, Kutateladze proposed a machinery for studying the extremal structure of convex sets of linear operators which was based on the theory of Kantorovich spaces.…
Order closed ideals in pre-Riesz spaces and their relationship to bands
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 equal their double…
Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces
We link conditional weak mixing and ergodicity of the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the…
Extension and factorization of Riesz n-morphisms on pre-Riesz spaces
On Disjointness, Bands and Projections in Partially Ordered Vector Spaces
Disjointness, bands, and band projections are a classical and essential part of the structure theory of vector lattices. If X is such a lattice, those notions seem – at first glance – intimately…
Tensor products in Riesz space theory as quotients of free spaces

References

SHOWING 1-10 OF 20 REFERENCES
The Archimedean ℓ-group tensor product
We introduce a construction (inZ F-set theory) for the Archimedean ℓ-group tensor product. We relate this tensor product to the existing ones in the theory of Archimedean vector lattices and ℓ-groups.
CONES IN THE TENSOR PRODUCT OF LOCALLY CONVEX LATTICES.
If E and F are locally convex lattices it is shown that the closure of the projective cone equals the biprojective cone for the projective topology on E 0 F and that this result cannot be extended to…
On the uniform density of C(X) ⊗ C(Y) in C(X × Y)
The vector lattice cover of certain partially ordered groups
In this paper we introduce the notion of Riesz homomorphism on Archimedean directed partially ordered groups and use it to study the vector lattice cover of such groups. 1991 Mathematics subject…
Positive Operators
TLDR
Book of positive operators, as an amazing reference becomes what you need to get, and book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.
The tensor product of Archimedean ordered vector spaces
Ordered Topological Tensor Products
Sherbert: Ordered topological tensor products
  • Proc. London Math. Soc
  • 1969
Tensor Products of Archimedean Partially Ordered Vector Spaces, Report MI-2010-01
  • Mathematical Institute, Leiden University
  • 2010
Completions in Riesz space theory
...
1
2
...