Local properties of polynomials on a Banach space
Aron, Richard M. ; Choi, Yun Sung ; Kim, Sung Guen ; Maestre, Manuel
Illinois J. Math., Tome 45 (2001) no. 4, p. 25-39 / Harvested from Project Euclid
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We introduce the concept of a smooth point of order $n$ of the closed unit ball of a Banach space $E$ and characterize such points for $E = c_0$, $L_p(\mu)$ ($1\leq p \le\infty$), and $C(K)$. We show that every locally uniformly rotund multilinear form and homogeneous polynomial on a Banach space $E$ is generated by locally uniformly rotund linear functionals on $E$. We also classify such points for $E = c_0$, $L_p(\mu)(1\leq p \le\infty)$, and $C(K)$.
Publié le : 2001-01-15
Classification:  46G25,  46B20,  46B28 
@article{1258138253,
     author = {Aron, Richard M. and Choi, Yun Sung and Kim, Sung Guen and Maestre, Manuel},
     title = {Local properties of polynomials on a Banach space},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 25-39},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138253}
}

Aron, Richard M.; Choi, Yun Sung; Kim, Sung Guen; Maestre, Manuel. Local properties of polynomials on a Banach space. Illinois J. Math., Tome 45 (2001) no. 4, pp.  25-39. http://gdmltest.u-ga.fr/item/1258138253/