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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. 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.
- All authors
- Zhang, F.
- Supervisor
- Doelman, A.
- Co-supervisor
- Gaans, O.W. van
- Committee
- Vaart, A. van der; Edixhoven, S.J.; Jeu, M. de; Pagter, B. de; Kaluuch, A.
- Qualification
- Doctor (dr.)
- Awarding Institution
- Mathematical Institute , Faculty of Science , Leiden University
- Date
- 2018-09-20
Funding
- Sponsorship
- Chinese scholarship council