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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Abstract

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

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

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1429286066

Digital Object Identifier
doi:10.15352/bjma/09-4-13

Mathematical Reviews number (MathSciNet)
MR3336892

Zentralblatt MATH identifier
1323.46002

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.bjma/1429286066


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