Strong proximinality and intersection properties of balls in Banach spaces

Jayanarayanan, C R and Paul, T (2015) Strong proximinality and intersection properties of balls in Banach spaces. Journal of Mathematical Analysis and Applications, 426 (2). pp. 1217-1231. ISSN 0022-247X

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Abstract

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z⊆Y⊆X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proximinal subspace Y of X is strongly proximinal in X if and only if Y⊥⊥ is strongly proximinal in X**. We also prove that in an abstract L1-space, the notions of strongly subdifferentiable points and quasi-polyhedral points coincide. We also give an example to show that M-ideals need not be ball proximinal. Moreover, we prove that in an L1-predual space, M-ideals are ball proximinal.

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IITH Creators:
IITH CreatorsORCiD
Paul, Thttp://orcid.org/0000-0002-2043-3888
Item Type: Article
Additional Information: The authors would like to thank Prof. T.S.S.R.K. Rao for many helpful discussions and valuable sugges- tions. A major part of this work was done when the second author was visiting Indian Statistical Institute, Bangalore as an NBHM post doctoral fellow and he would like to thank the NBHM for its financial support.
Uncontrolled Keywords: Proximinality; Strong proximinality; Ideal; Semi M-ideal; M-ideal
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 02 Mar 2015 05:15
Last Modified: 10 Aug 2017 08:26
URI: http://raiith.iith.ac.in/id/eprint/1365
Publisher URL: https://doi.org/10.1016/j.jmaa.2015.01.013
OA policy: http://www.sherpa.ac.uk/romeo/issn/0022-247X/
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