Extreme and exposed points of spaces of integral polynomials
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- by Christopher Boyd and Silvia Lassalle PDF
- Proc. Amer. Math. Soc. 138 (2010), 1415-1420 Request permission
Abstract:
We show that if $E$ is a real Banach space such that $E’$ has the approximation property and such that $\ell _1\not \hookrightarrow {\widehat \bigotimes _{n,s,\epsilon }} E$, then the set of extreme points of the unit ball of $\mathcal {P}_I(^nE)$ is equal to $\{\pm \phi ^n\colon \phi \in E’,\|\phi \|=1\}$. Under the additional assumption that $E’$ has a countable norming set, we see that the set of exposed points of the unit ball of $\mathcal {P}_I(^nE)$ is also equal to $\{\pm \phi ^n\colon \phi \in E’,\|\phi \|=1\}$.References
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Additional Information
- Christopher Boyd
- Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
- MR Author ID: 343443
- Email: Christopher.Boyd@ucd.ie
- Silvia Lassalle
- Affiliation: Departamento de Matemática, Pab. I – Cuidad Universitaria (FCEN), Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
- Email: slassall@dm.uba.ar
- Received by editor(s): February 3, 2009
- Received by editor(s) in revised form: August 11, 2009
- Published electronically: November 3, 2009
- Communicated by: Nigel J. Kalton
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1415-1420
- MSC (2010): Primary 46G25; Secondary 46B04
- DOI: https://doi.org/10.1090/S0002-9939-09-10158-2
- MathSciNet review: 2578533