Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE SEPARABLE WEAK BOUNDED APPROXIMATION PROPERTY

  • Lee, Keun Young (Institute for Ubiquitous Information Technology and Applications Konkuk University)
  • Received : 2012.08.18
  • Published : 2015.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

Keywords

References

  1. P. G. Cassaza, Approximate properties, In: W. B. Johnson, J. Lindenstrauss(eds.), Handbook of the Geometry of Banach Spaces, Volume 1, 271-316, Elsevier, 2001.
  2. C. Choi and J. M. Kim, Weak and quasi approximation properties in Banach spaces, J. Math. Anal. Appl. 316 (2006), no. 2, 722-735. https://doi.org/10.1016/j.jmaa.2005.05.013
  3. C. Choi and J. M. Kim, Hahn-Banach theorem for the compact convergence topology and applications to approximation properties, Houston J. Math. 37 (2011), no. 4, 1157-1164.
  4. T. Figiel and W. B. Johnson, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc. 41 (1973), 197-200. https://doi.org/10.1090/S0002-9939-1973-0341032-5
  5. A. Grothendieck, Produits tensoriels topologiques et espaces nucleires, Mem. Amer. Math. Soc. 16 (1955), no. 16, 140 pp.
  6. J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), no. 3, 304-311. https://doi.org/10.1016/0022-1236(79)90042-9
  7. K. Y. Lee, Dual spaces of compact operators space and the weak Radon-Nikodym property, Studia Math. 210 (2012), no. 3, 247-260. https://doi.org/10.4064/sm210-3-5
  8. A. Lima, O. Nygraard, and E. Oja, Isometric factorization of weakly compact operators and the approximation property, Israel J. Math. 119 (2000), 325-348. https://doi.org/10.1007/BF02810673
  9. A. Lima and E. Oja, The weak metric approximation property, Math. Ann. 333 (2005), no. 3, 471-484. https://doi.org/10.1007/s00208-005-0656-0
  10. J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain ${\ell}_1$ and whose duals are non-separable, Studia Math. 54 (1975), no. 1, 81-105. https://doi.org/10.4064/sm-54-1-81-105
  11. K. Musial, The weak Radon-Nikodym property in Banach spaces, Studia Math. 64 (1978), no. 2, 151-174.
  12. E. Oja, The impact of the Radon-Nikodym property on the weak bounded approximation property, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. 100 (2006), 325-331.
  13. R. A. Ryan, Introduction to Tensor Product of Banach Spaces, Springer, London, 2002.

Cited by

  1. Nuclear Pseudo-Differential Operators in Besov Spaces on Compact Lie Groups vol.23, pp.5, 2017, https://doi.org/10.1007/s00041-016-9512-8