Towards a Theory of Unbounded Locally Solid Riesz Spaces

Year 2019, Issue: 28, 20 - 27, 07.05.2019

Mehmet Vural

https://izlik.org/JA42WX76GW

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.
• M. A. Taylor, Unbounded topologies and uo-convergence in locally solid vector lattice,to appear.arXiv:1706.01575 [math.FA].
• [12] V. G. Troitsky, Measures of non-compactness of operators on Banach lattices, Positivity. 8(2),2004, 165-178
• A. W. Wickstead, Weak and unbounded order convergence in Banach lattices, J. Austral. Math.Soc. ser. A 24(3)(1977), 312-319.
• O.Zabeti,Unbounded absolute weak convergence in Banach lattices, to appear.arXiv:1608.02151[math.FA]