Illinois Journal of Mathematics

Local properties of polynomials on a Banach space

Richard M. Aron, Yun Sung Choi, Sung Guen Kim, and Manuel Maestre

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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 $C(K)$.

Article information

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

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
Secondary: 46B20: Geometry and structure of normed linear spaces 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]


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.

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