Factorization of multilinear operators defined on products of function spaces

ERDOĞAN E.

LINEAR & MULTILINEAR ALGEBRA, cilt.70, sa.2, ss.177-202, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/03081087.2020.1715334
  • Dergi Adı: LINEAR & MULTILINEAR ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.177-202
  • Anahtar Kelimeler: Banach function spaces, factorization, Multilinear and polynomial operators, symmetric operator, zero product preservation
  • Marmara Üniversitesi Adresli: Evet

Özet

This paper deals with multilinear operators acting in products of Banach spaces that factor through a canonical mapping. We prove some factorization theorems and characterizations by means of norm inequalities for multilinear operators defined on the n-fold Cartesian product of the space of bounded Borel measurable functions, respectively, products of Banach function spaces. These factorizations allow us to obtain integral dominations and lattice geometric properties and to present integral representations for abstract classes of multilinear operators. Finally, bringing together these ideas, some applications are shown, regarding for example summability properties and representation of multilinear maps as orthogonally additive n-homogeneous polynomials.