Year 2019, Volume , Issue 28, Pages 20 - 27 2019-05-07

Towards a Theory of Unbounded Locally Solid Riesz Spaces

Mehmet Vural [1]


We introduce the notion of unbounded locally solid Riesz spaces and we investigate its some fundamental properties.

Unbounded order convergence, Unbounded locally solid Riesz space.
  • 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]
Primary Language en
Subjects Mathematics
Journal Section Research Article
Authors

Author: Mehmet Vural
Institution: MUSTAFA KEMAL ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date : May 7, 2019

Bibtex @research article { jnt542836, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2019}, volume = {}, pages = {20 - 27}, doi = {}, title = {Towards a Theory of Unbounded Locally Solid Riesz Spaces}, key = {cite}, author = {Vural, Mehmet} }
APA Vural, M . (2019). Towards a Theory of Unbounded Locally Solid Riesz Spaces. Journal of New Theory , (28) , 20-27 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/45019/542836
MLA Vural, M . "Towards a Theory of Unbounded Locally Solid Riesz Spaces". Journal of New Theory (2019 ): 20-27 <https://dergipark.org.tr/en/pub/jnt/issue/45019/542836>
Chicago Vural, M . "Towards a Theory of Unbounded Locally Solid Riesz Spaces". Journal of New Theory (2019 ): 20-27
RIS TY - JOUR T1 - Towards a Theory of Unbounded Locally Solid Riesz Spaces AU - Mehmet Vural Y1 - 2019 PY - 2019 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 20 EP - 27 VL - IS - 28 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2019 ER -
EndNote %0 Journal of New Theory Towards a Theory of Unbounded Locally Solid Riesz Spaces %A Mehmet Vural %T Towards a Theory of Unbounded Locally Solid Riesz Spaces %D 2019 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 28 %R %U
ISNAD Vural, Mehmet . "Towards a Theory of Unbounded Locally Solid Riesz Spaces". Journal of New Theory / 28 (May 2019): 20-27 .
AMA Vural M . Towards a Theory of Unbounded Locally Solid Riesz Spaces. JNT. 2019; (28): 20-27.
Vancouver Vural M . Towards a Theory of Unbounded Locally Solid Riesz Spaces. Journal of New Theory. 2019; (28): 27-20.