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The separable weak bounded approximation property

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대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회보 (Bulletin of the KMS)|제52권 제1호|pp. 69-83

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키워드

the separable weak metric approximation propertyweak Radon-Nikod\'ym propertymetric approximation propertyfactorization lemma
주제분류수학

초록

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.

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.

참고문헌 (13)

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  2. C. Choi, "Weak and quasi approximation properties in Banach spaces", J. Math. Anal. Appl, 316(2), pp.722~735 (2006)
  3. C. Choi, "Hahn-Banach theorem for the compact convergence topology and applications to approximation properties", Houston J. Math, 37(4), pp.1157~1164 (2011)
  4. T. Figiel, "The approximation property does not imply the bounded approximation property", Proc. Amer. Math. Soc, 41, pp.197~200 (1973)
  5. A. Grothendieck, "Produits tensoriels topologiques et espaces nucl´eires", Mem. Amer. Math. Soc, 16(16), pp.140~ (1955)
  6. J. Johnson, "Remarks on Banach spaces of compact operators", J. Funct. Anal, 32(3), pp.304~311 (1979)
  7. K. Y. Lee, "Dual spaces of compact operators space and the weak Radon-Nikod´ym prop-erty", Studia Math, 210(3), pp.247~260 (2012)
  8. °A. Lima, "Isometric factorization of weakly compact operators and the approximation property", Israel J. Math, 119, pp.325~348 (2000)
  9. A. Lima, "The weak metric approximation property", Math. Ann, 333(3), pp.471~484 (2005)
  10. J. Lindenstrauss, "Examples of separable spaces which do not contain ℓ1 and whose duals are non-separable", Studia Math, 54(1), pp.81~105 (1975)
  11. K. Musial, "The weak Radon-Nikod´ym property in Banach spaces", Studia Math, 64(2), pp.151~174 (1978)
  12. E. Oja, "The impact of the Radon-Nikod´ym property on the weak bounded approximation property", Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math, 100, pp.325~331 (2006)
  13. R. A. Ryan, "Introduction to Tensor Product of Banach Spaces" (2002), Springer

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