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Year 2022, Volume: 51 Issue: 2, 483 - 493, 01.04.2022
https://doi.org/10.15672/hujms.961727

Abstract

References

  • [1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Berlin, Germany, Springer-Verlag, 2006.
  • [2] C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs 105, USA, Amer. Math. Soc., 2003.
  • [3] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Dordrecht, The Netherlands, Springer, 2006.
  • [4] C.D. Aliprantis and R. Tourky, Cones and Duality, Providence, Rhode Island, USA, Amer. Math. Soc., 2007.
  • [5] S. Alpay, B. Altin and C. Tonyali, On Property (b) of Vector Lattices, Positivity, 7, 135-139, 2003. doi: 10.1023/A:1025840528211
  • [6] B. Altin, On b-Weakly Compact Operators on Banach Lattices, Taiwan. J. Math. 11 (1), 143-150, 2007.
  • [7] B. Altin and N. Machrafi, Some Characterizations of KB-operators on Banach Lat- tices and Ordered Banach Spaces, Turkish J. Math. 44, 1736-1743, 2020.
  • [8] P.G. Dodds, o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214, 389-402, 1975.
  • [9] Z. Ercan, Interval-Bounded Operators and Order-Weakly Compact Operators of Riesz Spaces, Demonstr. Math. XXXI (4), 805-812, 1998.
  • [10] G. Köthe, Topological Vector Spaces I, Springer-Verlag New York Inc., 1969.
  • [11] P. Meyer-Nieberg, Banach Lattices, New York, USA, Springer, 1991.

A note on topologically b-order bounded sets and generalized b-weakly compact operators

Year 2022, Volume: 51 Issue: 2, 483 - 493, 01.04.2022
https://doi.org/10.15672/hujms.961727

Abstract

We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces. We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.

References

  • [1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Berlin, Germany, Springer-Verlag, 2006.
  • [2] C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs 105, USA, Amer. Math. Soc., 2003.
  • [3] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Dordrecht, The Netherlands, Springer, 2006.
  • [4] C.D. Aliprantis and R. Tourky, Cones and Duality, Providence, Rhode Island, USA, Amer. Math. Soc., 2007.
  • [5] S. Alpay, B. Altin and C. Tonyali, On Property (b) of Vector Lattices, Positivity, 7, 135-139, 2003. doi: 10.1023/A:1025840528211
  • [6] B. Altin, On b-Weakly Compact Operators on Banach Lattices, Taiwan. J. Math. 11 (1), 143-150, 2007.
  • [7] B. Altin and N. Machrafi, Some Characterizations of KB-operators on Banach Lat- tices and Ordered Banach Spaces, Turkish J. Math. 44, 1736-1743, 2020.
  • [8] P.G. Dodds, o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214, 389-402, 1975.
  • [9] Z. Ercan, Interval-Bounded Operators and Order-Weakly Compact Operators of Riesz Spaces, Demonstr. Math. XXXI (4), 805-812, 1998.
  • [10] G. Köthe, Topological Vector Spaces I, Springer-Verlag New York Inc., 1969.
  • [11] P. Meyer-Nieberg, Banach Lattices, New York, USA, Springer, 1991.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Nabil Machrafı 0000-0002-0667-6613

Birol Altın 0000-0002-1085-809X

Publication Date April 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 2

Cite

APA Machrafı, N., & Altın, B. (2022). A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics, 51(2), 483-493. https://doi.org/10.15672/hujms.961727
AMA Machrafı N, Altın B. A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics. April 2022;51(2):483-493. doi:10.15672/hujms.961727
Chicago Machrafı, Nabil, and Birol Altın. “A Note on Topologically B-Order Bounded Sets and Generalized B-Weakly Compact Operators”. Hacettepe Journal of Mathematics and Statistics 51, no. 2 (April 2022): 483-93. https://doi.org/10.15672/hujms.961727.
EndNote Machrafı N, Altın B (April 1, 2022) A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics 51 2 483–493.
IEEE N. Machrafı and B. Altın, “A note on topologically b-order bounded sets and generalized b-weakly compact operators”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, pp. 483–493, 2022, doi: 10.15672/hujms.961727.
ISNAD Machrafı, Nabil - Altın, Birol. “A Note on Topologically B-Order Bounded Sets and Generalized B-Weakly Compact Operators”. Hacettepe Journal of Mathematics and Statistics 51/2 (April 2022), 483-493. https://doi.org/10.15672/hujms.961727.
JAMA Machrafı N, Altın B. A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics. 2022;51:483–493.
MLA Machrafı, Nabil and Birol Altın. “A Note on Topologically B-Order Bounded Sets and Generalized B-Weakly Compact Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, 2022, pp. 483-9, doi:10.15672/hujms.961727.
Vancouver Machrafı N, Altın B. A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics. 2022;51(2):483-9.