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.
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.
Keywords
b-order bounded set order weakly compact operator b-weakly compact operator locally convex-solid Riesz space Fréchet lattice Banach 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 1, 2022 |
| Published in Issue | Year 2022 |