On discrete and continuous quotient Riesz spaces
- First Online:
- 62 Downloads
Order properties of quotient Riesz spaces E/N(f) by null ideals N(f) are investigated. We show relationships between properties of a Riesz space E and its order dual E~ and properties of quotients E/N(f) where f runs over some subspaces of E~. A characterization of metrizable locally convex topological Riesz spaces whose all quotients (by proper closed ideals) are discrete is also given.
KeywordsRiesz space Banach lattice Locally solid Riesz space Null ideal Order bounded operator
Mathematics Subject Classification (2000)46A40 46B42 46B45
Unable to display preview. Download preview PDF.
- 1.Aliprantis, C., Burkinshaw, O.: Locally Solid Riesz Spaces with Applications to Economics. Mathematical Surveys and Monographs, vol. 105, American Mathematical Society (2003)Google Scholar
- 4.Jameson, G.: Ordered Linear Spaces. Lecture Notes in Mathematics, vol. 141. Springer, Berlin (1970)Google Scholar
- 8.Wiatrowski, B.: On a structure of quotient Riesz spaces, Ph.D.Thesis, A. Mickiewicz University, Poznań (2006) (in Polish)Google Scholar
- 10.Wnuk W.: Banach lattices with order continuous norms, Advanced Topics in Mathematics. Polish Scientific Publishers PWN, Warsaw (1999)Google Scholar
- 12.Wnuk, W.: Selected topics in quotient Riesz spaces—a short survey. Proceedings of the International Symposium on Banach and Function Spaces II, Kitakyusiu, Japan 2006, Yokohama Publ., 243–276Google Scholar