## Illinois Journal of Mathematics

### Local properties of polynomials on a Banach space

#### Abstract

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 $C(K)$.

#### Article information

Source
Illinois J. Math., Volume 45, Number 1 (2001), 25-39.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138253

Digital Object Identifier
doi:10.1215/ijm/1258138253

Mathematical Reviews number (MathSciNet)
MR1849984

Zentralblatt MATH identifier
1001.46029

#### Citation

Aron, Richard M.; Choi, Yun Sung; Kim, Sung Guen; Maestre, Manuel. Local properties of polynomials on a Banach space. Illinois J. Math. 45 (2001), no. 1, 25--39. doi:10.1215/ijm/1258138253. https://projecteuclid.org/euclid.ijm/1258138253