JournalsprimsVol. 49, No. 1pp. 111–122

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
The Hadamard Product in the Space of Lorch Analytic Mappings cover
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Abstract

For a complex Banach algebra EE, let HL(E){\mathrm{H}}_L(E) be the space of the mappings from EE into EE that are analytic in the sense of Lorch, endowed with the Hadamard product and with the topology τb\tau_b of uniform convergence on the bounded subsets of EE. We study topological and algebraic properties of HL(E){\mathrm{H}}_L(E) in connection with the topological and algebraic properties of the underlying space EE. We also study algebraic and topological properties of the space of the sequences (an)nE(a_n)_n \subset E such that limnan1n=0.\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