On b-weakly demicompact operators on Banach lattices
Автор: Benkhaled Hedi, Jeribi Aref
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 4 т.25, 2023 года.
Бесплатный доступ
Aqzzouz and Elbour proved that an operator T on a Banach lattice E is b-weakly compact if and only if ∥Txn∥→0 as n→∞ for each b-order bounded weakly sequence {xn} in E+. In this present paper, we introduce and study new concept of operators that we call b-weakly demicompact, use it to generalize known classes of operators which defined by b-weakly compact operators. An operator T on a Banach lattice E is said to be b-weakly demicompact if for every b-order bounded sequence {xn} in E+ such that xn→0 in σ(E,E′) and ∥xn-Txn∥→0 as n→∞, we have ∥xn∥→0 as n→∞. As consequence, we obtain a characterization of KB-spaces in terms of b-weakly demicompact operators. After that, we investigate the relationships between b-weakly demicompact operators and some other classes of operators on Banach lattices espaciallly their relationships with demi Dunford-Pettis operators and order weakly demicompact operators.
Banach lattice, kb-space, b-weakly demicompact operator, order weakly demicompact operator, demi dunford-pettis operator
Короткий адрес: https://sciup.org/143180938
IDR: 143180938 | DOI: 10.46698/b8543-3760-0663-r
Список литературы On b-weakly demicompact operators on Banach lattices
- Alpay, S., Altn, B. and Tonyal, C. On Property (b) of Vector Lattices, Positivity, 2003, vol. 7, pp. 135-139. DOI: 10.1023/A:1025840528211.
- Alpay, S. and Altin, B. A Note on b-Weakly Compact Operators, Positivity, 2007, vol. 11, pp. 575-582. DOI: 10.1007/s11117-007-2110-x.
- Altin, B. On b-Weakly Compact Operators on Banach Lattices, Taiwanese Journal of Mathematics, 2007, vol. 11, no. 1, pp. 143-150.
- Aqzzouz, B. and Elbour, A. Some Properties of the Class of b-Weakly Compact Operators, Complex Analysis and Operator Theory, 2012, vol. 6, pp. 1139-1145. DOI: 10.1007/s11785-010-0108-z.
- Petryshyn, W. V. Construction of Fixed Points of Demicompact Mappings in Hilbert Space, Journal of Mathematical Analysis and Applications, 1996, vol. 14, no. 2, pp. 276-284. DOI: 10.1016/0022-247x(66)90027-8.
- Jeribi, A. Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, 2015.
- Krichen, B. and O'Regan, D. Weakly Demicompact Linear Operators and Axiomatic Measures of Weak Noncompactness, Mathematica Slovaca, 2019, vol. 69, no. 6, pp. 1403-1412. DOI: 10.1515/ms-2017-0317.
- Benkhaled, H., Hajji., M. and Jeribi, A. On the Class of Demi Dunford-Pettis Operators, Rendiconti del Circolo Matematico di Palermo Series 2, vol. 72, no. 2, 2022, pp. 901-911. DOI: 10.1007/s12215-021-00702-x
- Benkhaled, H., Elleuch, A. and Jeribi, A. The Class of Order Weakly Demicompact Operators, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2020, vol. 114, no. 2. DOI: 10.1007/s13398-020-00808-4.
- Aliprantis, C. D. and Burkinshaw, O. Positive Operators, Berlin, Springer, 2006.
- Meyer-Nieberg, P. Banach Lattices, Berlin, Heidelberg, New York, Springer-Verlag, 1991.
- Altin, B. Some Properties of b-Weakly Compact Operators, Gazi University Journal of Science, 2005, vol. 18, no. 3, pp. 391-395.
- Abramovich, Y. A. and Aliprantis, C. D. An Invitation to Operator Theory, Graduate Studies in Mathematics, vol. 50, Providence, American Mathematical Society, 2002.
- Aqzzouz, B., Elbour, A. and Hmichane, J. The Duality Problem for the Class of b-Weakly Compact Operators, Positivity, 2009, vol. 13, no. 4, pp. 683-692. DOI: 10.1007/s11117-008-2288-6.
- Aqzzouz, B., Moussa, M. and Hmichane, J. Some Characterizations of b-Weakly Compact Operators on Banach Lattices, Mathematical Reports, 2010, vol. 62, pp. 315-324.
