ANALYTIC SPACES DEFINED BY SYMMETRIC NORMING FUNCTIONS

Abstract

Let $c_0$ be the space of sequences converging to 0. A symmetric norming function (or briefly, s.n. function) is a function $\Phi$ from $c_0$ into nonnegative numbers with the properties of that in a norm, a normalizing criteria: $\Phi(1,0,0,\cdots) = 1$, and the symmetric condition: $\Phi(x_1,x_2,\cdots) = \Phi(x^*_1,x^*_2,\cdots)$, where $x^*_1, x^*_2, \cdots$ is the nonincreasing rearrangement of $|x_1|, |x_2|, \cdots$. In this paper, we will define spaces of analytic functions based on s.n. functions, which are generalization of the space $B^+_1$ in [2].