Towards a Theory of Unbounded Locally Solid Riesz Spaces
Abstract
We introduce the notion of unbounded locally solid Riesz spaces and we investigate its some fundamental properties.
Keywords
Unbounded order convergence,Unbounded locally solid Riesz space.
References
- Y.A.Dabboorasad,E.Y.Emelyanov,M.A.A.Marabeh, Order convergence in in nite-dimensionalvector lattices is not topological, to appear. arXiv:1705.09883[math.FA]
- Y.A.Dabboorasad,E.Y.Emelyanov,M.A.A.Marabeh, u -convergence in locally solid vector lat-tices, to appear. arXiv:1706.02006[math.FA]
- L. Deng, M. O'Brein and V. G. Troitsky Unbounded norm convergence in Banach lattices, Ar-civum Mathmematicum (BRNO), 51 (2015), 107-128.
- D.H. Fremlin, Topological Riesz spaces and Measure theory, Cambridge univ. Press, London andNew York, 1974
- N. Gao, V. G. Troitsky,F.Xhantos uo-convergence and its applications to Cesaro means in Banachlattices, Israel J. Math., to appear. arXiiv:1509.07914[math.FA]
- N.Gao, F. Xanthos Unbounded order convergence and application to martingales without proba-bility,J. Math. Anal. Appl.415 (2014), 931-947.
- N.Gao, Unbounded order convergence in Dual spaces , J. Math. Anal. Appl.,419,347-354,2014
- L. Hong, Locally Solid Topological Lattice Ordered Groups, Arcivum Mathmematicum (BRNO),51 (2015), 107-128.
- M.Kandic, M. Marabeh V. G. Troitsky, Unbounded Norm Topology in Banach Lattices J. Math.Anal. Appl., 451 (2017, no.1, 259-279)
- H. Nakano, Ergodic theorem in semiordered linear spaces, Ann. of. Math.(2), 49 (1948), 538-556.