Dissertation

Extension of Operators on Pre-Riesz Spaces

This thesis mainly extends the theory of positive operators on Riesz spaces to a setting of pre-Riesz spaces.

Author

Zhang, F.

Date

20 September 2018

Links

Thesis in Leiden Repository

This thesis mainly extends the theory of positive operators on Riesz spaces to a setting of pre-Riesz spaces. The theory of pre-Riesz space was established by M. van Haandel in 1993, which yields that every directed Archimedean partially ordered vector space (pre-Riesz space) owns a vector lattice cover, that is, it can be embedded order densely into a Riesz space. Then this theory was developed by O. van Gaans and A. Kalauch during 1999-2016. Based on that, we study some properties of operators on pre-Riesz spaces, e.g. disjointness preserving operator, compact operator, disjointness preserving semigroup, local generator, dissipativity etc. on pre-Riesz spaces, which extends the classical operator theories on Riesz spaces and Banach lattices.

• partially ordered vector spaces
• pre-riesz space
• riesz completion