# The Hadamard Product in the Space of Lorch Analytic Mappings

### Luiza A. Moraes

Universidade Federal do Rio de Janeiro, Brazil### Alex F. Pereira

Universidade Federal do Rio de Janeiro, Macaé, Brazil

## Abstract

For a complex Banach algebra $E$, let ${\mathrm{H}}_L(E)$ be the space of the mappings from $E$ into $E$ that are analytic in the sense of Lorch, endowed with the Hadamard product and with the topology $\tau_b$ of uniform convergence on the bounded subsets of $E$. We study topological and algebraic properties of ${\mathrm{H}}_L(E)$ in connection with the topological and algebraic properties of the underlying space $E$. We also study algebraic and topological properties of the space of the sequences $(a_n)_n \subset E$ such that $\underset{n\to\infty}{\lim}\Vert a_n\Vert^\frac{1}{n}=0.$

## Cite this article

Luiza A. Moraes, Alex F. Pereira, The Hadamard Product in the Space of Lorch Analytic Mappings. Publ. Res. Inst. Math. Sci. 49 (2013), no. 1, pp. 111–122

DOI 10.4171/PRIMS/98