Annals of Functional Analysis

A new characterization of the bounded approximation property

Ju Myung Kim and Keun Young Lee

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Abstract

We prove that a Banach space X has the bounded approximation property if and only if, for every separable Banach space Z and every injective operator T from Z to X, there exists a net (Sα) of finite-rank operators from Z to X with SαλT such that lim αSαzTz=0 for every zZ.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 672-677.

Dates
Received: 22 March 2016
Accepted: 24 June 2016
First available in Project Euclid: 5 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1475685113

Digital Object Identifier
doi:10.1215/20088752-3661116

Mathematical Reviews number (MathSciNet)
MR3555758

Zentralblatt MATH identifier
1360.46013

Subjects
Primary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Secondary: 47L20: Operator ideals [See also 47B10]

Keywords
bounded approximation property bounded compact approximation property separable Banach space

Citation

Kim, Ju Myung; Lee, Keun Young. A new characterization of the bounded approximation property. Ann. Funct. Anal. 7 (2016), no. 4, 672--677. doi:10.1215/20088752-3661116. https://projecteuclid.org/euclid.afa/1475685113


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References

  • [1] T. Figiel and W. B. Johnson, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc. 41 (1973), 197–200.
  • [2] W. B. Johnson, A complementary universal conjugate Banach space and its relation to the approximation problem, Israel J. Math. 13 (1972), 301–310.
  • [3] J. M. Kim and B. Zheng, The strong approximation property and the weak bounded approximation property, J. Funct. Anal. 266 (2014), no. 8, 5439–5447.
  • [4] K. Y. Lee, The separable weak bounded approximation property, Bull. Korean Math. Soc. 52 (2015), no. 1, 69–83.
  • [5] Å. Lima, O. Nygaard, and E. Oja, Isometric factorization of weakly compact operators and the approximation property, Israel J. Math. 119 (2000), 325–348.
  • [6] Å. Lima and E. Oja, The weak metric approximation property, Math. Ann. 333 (2005), no. 3, 471–484.
  • [7] J. Lindenstrauss, On nonseparable reflexive Banach spaces, Bull. Amer. Math. Soc. (N.S.) 72 (1966), 967–970.
  • [8] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I: Sequence Spaces, Ergeb. Math. Grenzgeb (3) 92, Springer, Berlin, 1977.
  • [9] E. Oja, The impact of the Radon-Nikod$\acute{y}$m property on the weak bounded approximation property, Rev. R. Acad. Cien. Exactas Fís. Nat. Ser. A. Mat. RACSAM 100 (2006), no. 1–2, 325–331.
  • [10] E. Oja, On a separable weak version of the bounded approximation property, Arch. Math. (Basel) 107 (2016), no. 2, 185–189.