Year 2022,
Volume: 5 Issue: 4, 234 - 239, 01.12.2022
Ayşegül Keten Çopur
,
Adalet Satar
References
- [1] S. Banach, Th´eorie Des Op´erations Lin´eaires, Monogr. Mat., Warsaw, 1932.
- [2] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, Mem. Amer. Math. Soc., 16 (1955). (French)
- [3] P. G. Casazza, Approximation Properties, in: W. B. Johnson, J. Lindenstrauss (Eds.), Handbook of the Geometry of Banach Spaces, Elsevier, Amsterdam, 1 (2001), 271-316.
- [4] C. Choi, J. M. Kim, Weak and quasi approximation properties in Banach Spaces, J. Math. Anal. Appl., 316(2) (2006), 722-735.
- [5] C. Choi, J. M. Kim, On dual and three space problems for the compact approximation property, J. Math. Anal. Appl., 323(1) (2006), 78-87.
- [6] J. M. Kim, On relations between weak approximation properties and their inheritances to subspaces, J. Math. Anal. Appl., 324(1) (2006), 721-727.
- [7] C. Choi, J. M. Kim, K. Y. Lee, Right and left weak approximation properties in Banach spaces, Canad. Math. Bull., 52(1) (2009), 28-38.
- [8] J. M. Kim, K. Y. Lee, Weak approximation properties of subspaces, Banach J. Math. Anal., 9(2) (2015), 248-252.
- [9] J. M. Kim, K. Y. Lee, A new characterization of the bounded approximation property, Ann. Funct. Anal., 7(4) (2016), 672-677.
- [10] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I, Sequence Spaces, Springer, Berlin, 1977.
- [11] D. P. Sinha, A. K. Karn, Compact operators whose adjoints factor through subspaces of lp, Studia Math., 150(1) (2002), 17-33.
- [12] J. M. Delgado, E. Oja, C. Pi˜neiro, E. Serrano, The p-approximation property in terms of density of finite rank operators, J. Math. Anal. Appl., 354(1) (2009), 159-164.
- [13] Y. S. Choi, J. M. Kim, The dual space of (L(X;Y); tp) and the p-approximation property, J. Funct. Anal., 259(9) (2010), 2437-2454.
- [14] C. J. Li, X. C. Fang, p-weak approximation property in Banach spaces, Chinese Ann. Math. Ser. A, 36(3) (2015), 247-256. (Chinese)
- [15] A. Keten, On the duality problem for the p-compact approximation property and its inheritance to subspaces, Konuralp J. Math., 7(2) (2019), 399-404.
- [16] J. M. Kim, The ideal of weakly p-compact operators and its approximation property for Banach spaces, Ann. Acad. Sci. Fenn. Math., 45(2) (2020), 863-876.
- [17] R. E. Megginson, An Introduction to Banach Space Theory, Springer, New York, 1998.
- [18] C. Choi, J. M. Kim, Locally convex vector topologies on B(X;Y), J. Korean Math. Soc., 45(6) (2008), 1677-1703.
- [19] N. J. Kalton, Locally complemented subspaces and Lp spaces for 0 < p < 1, Math. Nachr., 115 (1984), 71–97.
- [20] A. Lima, The metric approximation property, norm-one projections and intersection properties of balls, Israel J. Math., 84(3) (1993), 451-475.
Some Results on the $p$-Weak Approximation Property in Banach Spaces
Year 2022,
Volume: 5 Issue: 4, 234 - 239, 01.12.2022
Ayşegül Keten Çopur
,
Adalet Satar
Abstract
In this study, some existing results dealing with the weak approximation property of Banach spaces are considered for the $p$-weak approximation property. Also, an observation on the bounded weak approximation and the $p$-bounded weak approximation properties is given. Moreover, the proof of the solution of the duality problem for the $p$-weak approximation property which exists in the literature is given in a shorter way as an alternative.
References
- [1] S. Banach, Th´eorie Des Op´erations Lin´eaires, Monogr. Mat., Warsaw, 1932.
- [2] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, Mem. Amer. Math. Soc., 16 (1955). (French)
- [3] P. G. Casazza, Approximation Properties, in: W. B. Johnson, J. Lindenstrauss (Eds.), Handbook of the Geometry of Banach Spaces, Elsevier, Amsterdam, 1 (2001), 271-316.
- [4] C. Choi, J. M. Kim, Weak and quasi approximation properties in Banach Spaces, J. Math. Anal. Appl., 316(2) (2006), 722-735.
- [5] C. Choi, J. M. Kim, On dual and three space problems for the compact approximation property, J. Math. Anal. Appl., 323(1) (2006), 78-87.
- [6] J. M. Kim, On relations between weak approximation properties and their inheritances to subspaces, J. Math. Anal. Appl., 324(1) (2006), 721-727.
- [7] C. Choi, J. M. Kim, K. Y. Lee, Right and left weak approximation properties in Banach spaces, Canad. Math. Bull., 52(1) (2009), 28-38.
- [8] J. M. Kim, K. Y. Lee, Weak approximation properties of subspaces, Banach J. Math. Anal., 9(2) (2015), 248-252.
- [9] J. M. Kim, K. Y. Lee, A new characterization of the bounded approximation property, Ann. Funct. Anal., 7(4) (2016), 672-677.
- [10] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I, Sequence Spaces, Springer, Berlin, 1977.
- [11] D. P. Sinha, A. K. Karn, Compact operators whose adjoints factor through subspaces of lp, Studia Math., 150(1) (2002), 17-33.
- [12] J. M. Delgado, E. Oja, C. Pi˜neiro, E. Serrano, The p-approximation property in terms of density of finite rank operators, J. Math. Anal. Appl., 354(1) (2009), 159-164.
- [13] Y. S. Choi, J. M. Kim, The dual space of (L(X;Y); tp) and the p-approximation property, J. Funct. Anal., 259(9) (2010), 2437-2454.
- [14] C. J. Li, X. C. Fang, p-weak approximation property in Banach spaces, Chinese Ann. Math. Ser. A, 36(3) (2015), 247-256. (Chinese)
- [15] A. Keten, On the duality problem for the p-compact approximation property and its inheritance to subspaces, Konuralp J. Math., 7(2) (2019), 399-404.
- [16] J. M. Kim, The ideal of weakly p-compact operators and its approximation property for Banach spaces, Ann. Acad. Sci. Fenn. Math., 45(2) (2020), 863-876.
- [17] R. E. Megginson, An Introduction to Banach Space Theory, Springer, New York, 1998.
- [18] C. Choi, J. M. Kim, Locally convex vector topologies on B(X;Y), J. Korean Math. Soc., 45(6) (2008), 1677-1703.
- [19] N. J. Kalton, Locally complemented subspaces and Lp spaces for 0 < p < 1, Math. Nachr., 115 (1984), 71–97.
- [20] A. Lima, The metric approximation property, norm-one projections and intersection properties of balls, Israel J. Math., 84(3) (1993), 451-475.