Product Factorable Multilinear Operators defined on Sequence Spaces


ERDOĞAN E.

Communications Faculty of Sciences University of Ankara SeriesSeries A1: Mathematics and Statistics, vol.69, no.2, pp.152-166, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.31801/cfsuasmas.752148
  • Title of Journal : Communications Faculty of Sciences University of Ankara SeriesSeries A1: Mathematics and Statistics
  • Page Numbers: pp.152-166
  • Keywords: Sequence spaces, multilinear operators, factorization, zero product preserving map, polynomials, ORTHOGONALLY ADDITIVE POLYNOMIALS, BILINEAR OPERATORS, MAPS, ALGEBRAS

Abstract

We prove a factorization theorem for multilinear operators acting in topological products of spaces of (scalar) p-summable sequences through a product. It is shown that this class of multilinear operators called product factorable maps coincides with the well-known class of the zero product preserving operators. Due to the factorization, we obtain compactness and summability properties by using classical functional analysis tools. Besides, we give some isomorphisms between spaces of linear and multilinear operators, and representations of some classes of multilinear maps as n-homogeneous orthogonally additive polynomials.