Under a suitable renorming every nonreflexive Banach space has a finite subset without a Steiner point

Author V. Kadets
vova1kadets@yahoo.com
Kharkiv National University

Abstract We present a refinement of the recent Borodin's example of a finite set without a Steiner point. Namely, we show that under a suitable renorming such an example exists in every nonreflexive Banach space.
Keywords Steiner point of a finite set; Banach space; equivalent norm
DOI
doi:10.30970/ms.36.2.197-200
Reference 1. Borodin P.A., An example of nonexistence of a Steiner point in a Banach space, Mat. Zametki, 87 (2010), №4, 514–518. (in Russian) English transl. in Math. Notes 87 (2010), №4, 485–488.

 2. Kadets V.M., A course in functional analysis, Karazin Kharkiv National University, 2006, 607p. (in Russian)

 3. Lindenstrauss J., Tzafriri L., Classical Banach spaces. I. Sequence spaces, Springer-Verlag, Berlin-New York, 1977, 188p.
Pages 197-200
Volume 36
Issue 2
Year 2011
Journal Matematychni Studii
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