Advances in Operator Theory

The AHSp is inherited by $E$-summands

Francisco García-Pacheco

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In this short note we prove that the Approximate Hyperplane Series property (AHSp) is hereditary to $E$-summands via characterizing the $E$-projections.

Article information

Adv. Oper. Theory, Volume 2, Number 1 (2017), 17-20.

Received: 15 October 2016
Accepted: 30 December 2016
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B07: Local theory of Banach spaces 46B03: Isomorphic theory (including renorming) of Banach spaces

projection complemented norm-attaining


García-Pacheco, Francisco. The AHSp is inherited by $E$-summands. Adv. Oper. Theory 2 (2017), no. 1, 17--20. doi:10.22034/aot.1610.1033.

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  • M. D. Acosta, R. M. Aron, D. García, and M. Maestre, The Bishop-Phelps-Bollobás Theorem for operators, J. Funct. Anal. 254 (2008), no. 11, 2780–2799.
  • M. D. Acosta, R. M. Aron, and F. J. García-Pacheco, The approximate hyperplane series property and related properties, Banach J. Math. Anal. (to appear).
  • Y. S. Choi, S. K. Kim, H. J. Lee, and M. Martín, On Banach spaces with the approximate hyperplane series property, Banach J. Math. Anal. 9 (2015), no. 4, 243–258.