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LOCALLY CONVEX VECTOR TOPOLOGIES ON B(X, Y )

김주명|최창선
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회지 (Journal of the KMS)|제45권 제6호|pp. 1677-1703

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참고문헌

키워드

bounded linear operatorlocally convex vector topologyapproximation property
주제분류수학

초록

In this paper, we introduce and study various locally convex vector topologies on the space of bounded linear operators between Banach spaces. We also apply these topologies to approximation properties.

Abstract

In this paper, we introduce and study various locally convex vector topologies on the space of bounded linear operators between Banach spaces. We also apply these topologies to approximation properties.

참고문헌 (14)

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  3. C. Choi, "Weak and quasi approximation properties in Banach spaces", Journal of Mathematical Analysis and Applications, 316(2), pp.722~735 (2006)
  4. N. Dunford, "Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7" (1958), Interscience Publishers, Inc.
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  6. A. Grothendieck, "Produits tensoriels topologiques et espaces nucl´eaires", Memoirs of the American Mathematical Society, 16 (1955)
  7. N. J. Kalton, "Spaces of compact operators", Mathematische Annalen, 208, pp.267~278 (1974)
  8. J. M. Kim, "Compactness in B(X)", Journal of Mathematical Analysis and Applications, 320(2), pp.619~631 (2006)
  9. J. M. Kim, "Dual problems for weak and quasi approximation properties", Journal of Mathematical Analysis and Applications, 321(2), pp.569~575 (2006)
  10. J. M. Kim, "On relations between weak approximation properties and their inheritances to subspaces", Journal of Mathematical Analysis and Applications, 324(1), pp.721~727 (2006)
  11. J. M. Kim, "Compact adjoint operators and approximation properties", Journal of Mathematical Analysis and Applications, 327(1), pp.257~268 (2007)
  12. R. E. Megginson, "An Introduction to Banach Space Theory, Graduate Texts in Mathematics", pp.183~ (1998), Springer-Verlag
  13. R. A. Ryan, "Introduction to Tensor Products of Banach Spaces, Springer Monographs in Mathematics" (2002), Springer-Verlag London, Ltd.
  14. G. A. Willis, "The compact approximation property does not imply the approximation property", Studia Mathematica, 103(1), pp.99~108 (1992)

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