Extreme and Exposed Points of Spaces of Integral Polynomials

BOYD, C., LASSALLE, S.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

American Mathematical Society

Lugar: Providence RI ; Año: 2010 vol. 138 p. 1415 - 1420

0002-9939

We show that if $E$ is a real Banach space such that $E´$ has theapproximation property and such that $ell_1 othookrightarrow {widehatigotimes_{n,s,epsilon}} E$ then the set of extremepoints of the unit ball of $mathcal{P}_I(^nE)$ is equal to${pmphi^ncolon phiin E´,|phi|=1}$. 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 ${pmphi^ncolon phiin E´,|phi|=1}$.