Banach Journal of Mathematical Analysis

On Banach spaces with the approximate hyperplane series property

Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, and Miguel Martin

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We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop--Phelps--Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of $w^*$-continuous operators and other related results.

Article information

Banach J. Math. Anal., Volume 9, Number 4 (2015), 243-258.

First available in Project Euclid: 17 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B04: Isometric theory of Banach spaces 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10]

Banach space approximation norm-attaining operators Bishop--Phelps--Bollob\'{a}s theorem


Choi, Yun Sung; Kim, Sun Kwang; Lee, Han Ju; Martin, Miguel. On Banach spaces with the approximate hyperplane series property. Banach J. Math. Anal. 9 (2015), no. 4, 243--258. doi:10.15352/bjma/09-4-13.

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