Unicellularity of the multiplication operator on Banach spaces of formal power series

B. Yousefi¹

¹ College of Sciences Shiraz University Shiraz 71454, Iran

Studia Mathematica, Tome 147 (2001) no. 3, pp. 201-209

Résumé

Let $\{\beta(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers and $1 \leq p \infty$. We consider the space $\ell^{p}(\beta)$ of all power series $f(z)\hskip-2pt =\hskip-2pt \sum^{\infty}_{n=0} \skew4\widehat{f}(n)z^{n}$ such that $\sum_{n=0}^{\infty} |\skew4\widehat{f}(n)|^{p}|\beta(n)|^{p} \infty$. We give some sufficient conditions for the multiplication operator, $M_{z}$, to be unicellular on the Banach space $\ell^{p}(\beta)$. This generalizes the main results obtained by Lu Fang [1].

Détail

DOI : 10.4064/sm147-3-1

Keywords: beta infty sequence positive numbers leq infty consider space ell beta power series hskip hskip sum infty skew widehat sum infty skew widehat beta infty sufficient conditions multiplication operator unicellular banach space ell beta generalizes main results obtained fang nbsp