Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 2, 399 - 404, 15.10.2019

Öz

Kaynakça

  • [1] R.M. Aron, M. Maestre, P. Rueda: p-Compact holomorphic mappings, RACSAM 104 (2) (2010), 353-364.
  • [2] R.M. Aron, P. Rueda: p-Compact homogeneous polynomials from an ideal point of view, Contemporary Mathematics, Amer. Math. Soc. 547 (2011), 61-71.
  • [3] R.M. Aron, E. C alıskan, D. Garcia, M. Maestre: Behavior of holomorphic mappings on p-compact sets in a Banach space, Trans. Amer. Math. Soc., 368 (2016), 4855-4871.
  • [4] P.G. Casazza: Approximation properties, in: W.B. Johnson, J. Lindenstrauss (Eds.), Handbook of the Geometry of Banach Spaces, vol. 1, Elsevier, Amsterdam (2001), 271-316.
  • [5] P.G. Casazza, H. Jarchow: Self-induced compactness in Banach spaces, Proc. Royal Soc. Edinburgh, 126A (1996), 355-362.
  • [6] C. Choi, J.M. Kim: On dual and three space problems for the compact approximation property, J. Math. Anal. Appl. 323 (2006), 78-87.
  • [7] C. Choi, J.M. Kim: Weak and quasi-approximation properties in Banach Spaces, J. Math. Anal. Appl. 316 (2006), 722-735.
  • [8] Y.S. Choi, J.M. Kim: The dual space of (L(X;Y); tp) and the p-approximation property, J. Funct. Anal. 259 (2010), 2437-2454.
  • [9] L. Changjing, F. Xiaochun: p-Weak approximation property in Banach spaces, Chinese Annals of Mathematics, Series A, 36 (3) (2015), 247-256.
  • [10] E. C alıs¸kan: The bounded approximation property for the predual of the space of bounded holomorphic mappings, Studia Math. 177 (3) (2006), 225-233.
  • [11] E. C alıs¸kan, A. Keten: Uniform factorization for p-compact sets of p-compact linear operators, J. Math. Anal. Appl. 437 (2) (2016), 1058-1069.
  • [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 (2009), 159-164.
  • [13] J.M. Delgado, C. Pineiro, E. Serrano: Density of finite rank operators in the Banach space of p-compact operators, J. Math. Anal. Appl. 370 (2010), 498-505.
  • [14] A. Grothendieck: Produits tensoriels topologiques et espaces nucl´eaires, Mem. Amer. Math. Soc. 16 (1955).
  • [15] J.M. Kim: On relations between weak approximation poperties and their inheritances to subspaces, J. Math. Anal. Appl. 324 (2006), 721-727.
  • [16] S. Lassalle, P. Turco: On p-compact mappings and the p-approximation property, J. Math. Anal. Appl. 389 (2012), 1204-1221.
  • [17] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces I, Sequence Spaces, Springer, Berlin, 1977.
  • [18] E. Oja: A remark on the approximation of p-compact operators by finite-rank operators, J. Math. Anal. Appl. 387 (2012), 949-952.
  • [19] D.P. Sinha, A.K. Karn: Compact operators whose adjoints factor through subspaces of lp, Studia Math. 150 (2002), 17-33.
  • [20] D.P. Sinha, A.K. Karn: Compact operators which factor through subspaces of lp, Math. Nachr. 281 (2008), 412-423.

On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces

Yıl 2019, Cilt: 7 Sayı: 2, 399 - 404, 15.10.2019

Öz

In this paper, for $1<p<\infty$ we define the $v_p$ and $v_{p}^{*}$-topologies on the space of bounded linear operators between Banach spaces, and by way of these topologies we introduce the properties $v_{p}^{*}\text D$ and $\text Bv_{p}^{*}\text D$ for the dual space $E^{'}$. Under the assumption of the property $v_{p}^{*}\text D$  on the dual space $E^{'}$, we obtain a solution of the duality problem for the $p$-CAP with $2<p<\infty$. We show that, if $M$ is a closed subspace of a Banach space $E$ such that $M^{\perp}$ is complemented in the dual space $E^{'}$, then $M$ has the $p$-CAP (respectively, BCAP) whenever $E$ has the $p$-CAP (respectively, BCAP) and the dual space $M^{'}$ has the $v_{p}^{*}\text D$ (respectively, $\text Bv_{p}^{*}\text D$).

Kaynakça

  • [1] R.M. Aron, M. Maestre, P. Rueda: p-Compact holomorphic mappings, RACSAM 104 (2) (2010), 353-364.
  • [2] R.M. Aron, P. Rueda: p-Compact homogeneous polynomials from an ideal point of view, Contemporary Mathematics, Amer. Math. Soc. 547 (2011), 61-71.
  • [3] R.M. Aron, E. C alıskan, D. Garcia, M. Maestre: Behavior of holomorphic mappings on p-compact sets in a Banach space, Trans. Amer. Math. Soc., 368 (2016), 4855-4871.
  • [4] P.G. Casazza: Approximation properties, in: W.B. Johnson, J. Lindenstrauss (Eds.), Handbook of the Geometry of Banach Spaces, vol. 1, Elsevier, Amsterdam (2001), 271-316.
  • [5] P.G. Casazza, H. Jarchow: Self-induced compactness in Banach spaces, Proc. Royal Soc. Edinburgh, 126A (1996), 355-362.
  • [6] C. Choi, J.M. Kim: On dual and three space problems for the compact approximation property, J. Math. Anal. Appl. 323 (2006), 78-87.
  • [7] C. Choi, J.M. Kim: Weak and quasi-approximation properties in Banach Spaces, J. Math. Anal. Appl. 316 (2006), 722-735.
  • [8] Y.S. Choi, J.M. Kim: The dual space of (L(X;Y); tp) and the p-approximation property, J. Funct. Anal. 259 (2010), 2437-2454.
  • [9] L. Changjing, F. Xiaochun: p-Weak approximation property in Banach spaces, Chinese Annals of Mathematics, Series A, 36 (3) (2015), 247-256.
  • [10] E. C alıs¸kan: The bounded approximation property for the predual of the space of bounded holomorphic mappings, Studia Math. 177 (3) (2006), 225-233.
  • [11] E. C alıs¸kan, A. Keten: Uniform factorization for p-compact sets of p-compact linear operators, J. Math. Anal. Appl. 437 (2) (2016), 1058-1069.
  • [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 (2009), 159-164.
  • [13] J.M. Delgado, C. Pineiro, E. Serrano: Density of finite rank operators in the Banach space of p-compact operators, J. Math. Anal. Appl. 370 (2010), 498-505.
  • [14] A. Grothendieck: Produits tensoriels topologiques et espaces nucl´eaires, Mem. Amer. Math. Soc. 16 (1955).
  • [15] J.M. Kim: On relations between weak approximation poperties and their inheritances to subspaces, J. Math. Anal. Appl. 324 (2006), 721-727.
  • [16] S. Lassalle, P. Turco: On p-compact mappings and the p-approximation property, J. Math. Anal. Appl. 389 (2012), 1204-1221.
  • [17] J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces I, Sequence Spaces, Springer, Berlin, 1977.
  • [18] E. Oja: A remark on the approximation of p-compact operators by finite-rank operators, J. Math. Anal. Appl. 387 (2012), 949-952.
  • [19] D.P. Sinha, A.K. Karn: Compact operators whose adjoints factor through subspaces of lp, Studia Math. 150 (2002), 17-33.
  • [20] D.P. Sinha, A.K. Karn: Compact operators which factor through subspaces of lp, Math. Nachr. 281 (2008), 412-423.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Ayşegül Keten 0000-0002-7973-946X

Yayımlanma Tarihi 15 Ekim 2019
Gönderilme Tarihi 5 Nisan 2019
Kabul Tarihi 16 Mayıs 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 2

Kaynak Göster

APA Keten, A. (2019). On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces. Konuralp Journal of Mathematics, 7(2), 399-404.
AMA Keten A. On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces. Konuralp J. Math. Ekim 2019;7(2):399-404.
Chicago Keten, Ayşegül. “On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces”. Konuralp Journal of Mathematics 7, sy. 2 (Ekim 2019): 399-404.
EndNote Keten A (01 Ekim 2019) On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces. Konuralp Journal of Mathematics 7 2 399–404.
IEEE A. Keten, “On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces”, Konuralp J. Math., c. 7, sy. 2, ss. 399–404, 2019.
ISNAD Keten, Ayşegül. “On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces”. Konuralp Journal of Mathematics 7/2 (Ekim 2019), 399-404.
JAMA Keten A. On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces. Konuralp J. Math. 2019;7:399–404.
MLA Keten, Ayşegül. “On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces”. Konuralp Journal of Mathematics, c. 7, sy. 2, 2019, ss. 399-04.
Vancouver Keten A. On The Duality Problem for the $p$-Compact Approximation Property and Its Inheritance to Subspaces. Konuralp J. Math. 2019;7(2):399-404.
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