Multi-Smooth Points of Finite Order

Abstract

A point $x$ of the unit sphere $S(X)$ of the Banach space $X$ is called a multi-smooth point of order $n$ if there exist exactly $n$-independent continuous linear functionals $g_{1}, \ldots , g_{n}$, in $S($ $X^*)$, the unit sphere of the dual of $X$, such that $g_{i}(x)=1$, for $1\leq i\leq n$. The object of this paper is to characterize multi-smooth points of some function and operator spaces.