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Towards a Theory of Unbounded Locally Solid Riesz Spaces

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

Abstract

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

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

Abstract

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]
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mehmet Vural

Publication Date May 7, 2019
Submission Date March 21, 2019
Published in Issue Year 2019 Issue: 28

Cite

APA Vural, M. (2019). Towards a Theory of Unbounded Locally Solid Riesz Spaces. Journal of New Theory(28), 20-27.
AMA Vural M. Towards a Theory of Unbounded Locally Solid Riesz Spaces. JNT. May 2019;(28):20-27.
Chicago Vural, Mehmet. “Towards a Theory of Unbounded Locally Solid Riesz Spaces”. Journal of New Theory, no. 28 (May 2019): 20-27.
EndNote Vural M (May 1, 2019) Towards a Theory of Unbounded Locally Solid Riesz Spaces. Journal of New Theory 28 20–27.
IEEE M. Vural, “Towards a Theory of Unbounded Locally Solid Riesz Spaces”, JNT, no. 28, pp. 20–27, May 2019.
ISNAD Vural, Mehmet. “Towards a Theory of Unbounded Locally Solid Riesz Spaces”. Journal of New Theory 28 (May 2019), 20-27.
JAMA Vural M. Towards a Theory of Unbounded Locally Solid Riesz Spaces. JNT. 2019;:20–27.
MLA Vural, Mehmet. “Towards a Theory of Unbounded Locally Solid Riesz Spaces”. Journal of New Theory, no. 28, 2019, pp. 20-27.
Vancouver Vural M. Towards a Theory of Unbounded Locally Solid Riesz Spaces. JNT. 2019(28):20-7.


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