Lattice Lipschitz superposition operators on Banach function spaces

Creative Commons License

Arnau R., Calabuig J. M., ERDOĞAN E., Sánchez Pérez E. A.

Journal of Mathematical Analysis and Applications, cilt.546, sa.2, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 546 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.jmaa.2025.129233
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Banach function space, Diagonal map, Lattice Lipschitz, Lipschitz operator
  • Marmara Üniversitesi Adresli: Evet

Özet

We analyze and characterize the notion of lattice Lipschitz operator when defined between Banach function spaces. After showing some general results, we restrict our attention to the case of those Lipschitz operators which are representable by pointwise composition with a strongly measurable function. Mimicking the classical definition and characterizations of (linear) multiplication operators between Banach function spaces, we show that under certain conditions the requirement for a diagonal Lipschitz operator to be well-defined between two such spaces X(μ) and Y(μ) is that it can be represented by a strongly measurable function which belongs to the Bochner space M(X,Y)(μ,Lip0(R)). Here, M(X,Y) is the space of multiplication operators between X(μ) and Y(μ), and Lip0(R) is the space of real-valued Lipschitz maps with real variable that are equal to 0 in 0. This opens the door to a better understanding of these maps, as well as finding the relation of these operators to some normed tensor products and other classes of maps.