Complex Vector Lattices: Tensor Products And Multilinear Maps

In this thesis, we study completions of Archimedean real vector lattices relative to any nonempty set of continuous positively homogeneous functions defined on Rn. Examples of such completions include square mean closed vector lattices and geometric mean closed vector lattices. These functional completions lead to a vector lattice complexification of any Archimedean real vector lattice. Unlike the vector space complexification of an Archimedean real vector lattice, the vector lattice complexification always results in an Archimedean complex vector lattice. For example, we prove that the vector space complexification of the Fremlin tensor product C(X)⊗C(Y) is not a complex vector lattice when X and Y are uncountable metrizable compact spaces. The vector lattice complexification is employed to construct an Archimedean complex vector lattice tensor product, powers of Archimedean complex vector lattices, and the symmetric (antisymmetric) Archimedean complex vector lattice tensor product. We use tensor products and powers to develop a theory for various multilinear maps between Archimedean complex vector lattices. Finally, we prove the Cauchy-Schwarz Inequality for sesquilinear maps from a complex vector space to various types of Archimedean complex vector lattices.

Name thesis:degree_name

Ph.D. in Mathematics

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Schwanke, Christopher Michael

Contributors dc:contributor

• Gerard Buskes
• Bahram Alidaee
• Sandra Spiroff

• Complexification
• Functional Completion
• Multilinear Map
• Tensor Product
• Vector Lattice
• Mathematics

Repository record dc:identifier

https://egrove.olemiss.edu/etd/1068

OAI identifier oai:identifier

oai:egrove.olemiss.edu:etd-2067