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A characterization of bounded convex approximation properties

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Abstract

The characterization of bounded approximation properties defined by arbitrary operator ideals due to Oja is extended to bounded convex approximation properties. As an application, it is shown that the unique extension property of a Banach space X enables to lift the metric convex approximation property from a Banach space X to its dual space X*.

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References

  1. N. Dunford and J.T. Schwartz, Linear Operators. Part 1: General Theory, Wiley-Interscience, New York, 1958.

  2. T. Figiel, W.B. Johnson, and A. Pełczyński, Some approximation properties of Banach spaces and Banach lattices, Israel J. Math. 183 (2011), 199–231.

  3. Godefroy G., Saphar P.D.: Normes lisses et propriété d’approximation métrique. C. R. Acad. Sci. Paris Sér. I Math. 299, 753–756 (1984)

    MathSciNet  MATH  Google Scholar 

  4. Godefroy G., Saphar P.D.: Duality in spaces of operators and smooth norms on Banach spaces. Illinois J. Math. 32, 672–695 (1988)

    MathSciNet  MATH  Google Scholar 

  5. Johnson W.B., Oikhberg T.: Separable lifting property and extensions of local reflexivity. Illinois J. Math. 45, 123–137 (2001)

    MathSciNet  MATH  Google Scholar 

  6. Lissitsin A., Mikkor K., Oja E.: Approximation properties defined by spaces of operators and approximability in operator topologies. Illinois J. Math. 52, 563–582 (2008)

    MathSciNet  MATH  Google Scholar 

  7. Lissitsin A., Oja E.: The convex approximation property of Banach spaces. J. Math. Anal. Appl. 379, 616–626 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Oja E.: Lifting bounded approximation properties from Banach spaces to their dual spaces. J. Math. Anal. Appl. 323, 666–679 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Oikhberg T., Rosenthal H.P.: Extension properties for the space of compact operators. J. Funct. Anal. 179, 251–308 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Oja E., Treialt S.: Some duality results on bounded approximation properties of pairs. Studia Math. 217, 79–94 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Oja E., Veidenberg S.: Lifting convex approximation properties from Banach spaces to their dual spaces and the related local reflexivity. J. Math. Anal. Appl. 436, 729– (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. H.H. Schaefer and M.P. Wolff, Topological Vector Spaces, Springer, New York, 1999.

  13. Zolk I.: The Johnson–Schechtman space has the 6-bounded approximation property. J. Math. Anal. Appl. 358, 493–495 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Silja Veidenberg

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  1. Silja Veidenberg
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Correspondence to Silja Veidenberg.

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Veidenberg, S. A characterization of bounded convex approximation properties. Arch. Math. 107, 523–529 (2016). https://doi.org/10.1007/s00013-016-0952-9

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  • DOI: https://doi.org/10.1007/s00013-016-0952-9

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