Extension of operators on pre-Riesz spaces

Leiden Repository

Extension of operators on pre-Riesz spaces

Type: Doctoral Thesis
Title: Extension of operators on pre-Riesz spaces
Author: Zhang, F.
Issue Date: 2018-09-20
Keywords: Partially ordered vector spaces
Pre-Riesz space
Riesz completion
Abstract: 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.
Promotor: Supervisor: Doelman A. Co-Supervisor: Gaans O.W. van
Faculty: Faculty of Science
University: Leiden University
Handle: http://hdl.handle.net/1887/65567

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