Tensor products of measurable Banach bundles
Year: 2026
Type: article
Abstract: We study injective and projective tensor products of measurable Banach bundles. More precisely, given two separable measurable Banach bundles $$\textbf{E}$$ E , $$\textbf{F}$$ F defined over a probability space $$(\textrm{X},\Sigma ,\mathfrak {m})$$ ( X , Σ , m ) , we construct two measurable Banach bundles $$\textbf{E}\hat{\otimes }_\varepsilon \textbf{F}$$ E ⊗ ^ ε F and $$\textbf{E}\hat{\otimes }_\pi \textbf{F}$$ E ⊗ ^ π F over $$(\textrm{X},\Sigma ,\mathfrak {m})$$ ( X , Σ , m ) , such that $$\Gamma (\textbf{E}\hat{\otimes }_\varepsilon \textbf{F})\cong \Gamma (\textbf{E})\hat{\otimes }_\varepsilon \Gamma (\textbf{F})$$ Γ ( E ⊗ ^ ε F ) ≅ Γ ( E ) ⊗ ^ ε Γ ( F ) and $$\Gamma (\textbf{E}\hat{\otimes }_\pi \textbf{F})\cong \Gamma (\textbf{E})\hat{\otimes }_\pi \Gamma (\textbf{F})$$ Γ ( E ⊗ ^ π F ) ≅ Γ ( E ) ⊗ ^ π Γ ( F ) , where $$\textbf{G}\mapsto \Gamma (\textbf{G})$$ G ↦ Γ ( G ) is the map assigning to a measurable Banach bundle $$\textbf{G}$$ G
Source: Annals of Functional Analysis
Authors: Milica Caković, Danka Lučić, Enrico Pasqualetto
Institutions: University of Novi Sad, University of Jyväskylä
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7147140413