Boundaries and polyhedral Banach spaces
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- by V. P. Fonf, R. J. Smith and S. Troyanski PDF
- Proc. Amer. Math. Soc. 143 (2015), 4845-4849 Request permission
Abstract:
We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X\to Y$ is a bounded linear operator such that $T^*(Y^*)$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral space. Some corollaries of this result are presented.References
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Additional Information
- V. P. Fonf
- Affiliation: Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva, Israel
- MR Author ID: 190586
- Email: fonf@math.bgu.ac.il
- R. J. Smith
- Affiliation: School of Mathematical and Statistical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
- Email: richard.smith@maths.ucd.ie
- S. Troyanski
- Affiliation: Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo (Murcia), Spain — and — Institute of Mathematics and Informatics, Bulgarian Academy of Science, bl.8, acad. G. Bonchev str. 1113 Sofia, Bulgaria
- MR Author ID: 174580
- Email: stroya@um.es
- Received by editor(s): March 31, 2004
- Received by editor(s) in revised form: September 8, 2014
- Published electronically: May 8, 2015
- Additional Notes: The first author was supported by Israel Science Foundation, Grant 209/09. The second and third authors were supported financially by Science Foundation Ireland under Grant Number ‘SFI 11/RFP.1/MTH/3112’. The third author was also supported by FEDER-MCI MTM2011-22457 and by the Bulgarian National Scientific Fund DFNI-I02/10.
- Communicated by: Thomas Schlumprecht
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4845-4849
- MSC (2010): Primary 46B20
- DOI: https://doi.org/10.1090/proc/12644
- MathSciNet review: 3391042