Tensor products of measurable Banach bundles
Milica Cakovi\'c, Danka Lu\v{c}i\'c, Enrico Pasqualetto

TL;DR
This paper constructs measurable Banach bundles representing tensor products of modules over a probability space, providing a fiberwise approach to understanding injective and projective tensor products in this setting.
Contribution
It introduces a method to realize tensor products of measurable Banach bundles via their sections, linking module tensor products to bundle tensor products fiberwise.
Findings
Constructed measurable Banach bundles for tensor products
Established isomorphisms between bundle sections and module tensor products
Provided fiberwise representation of tensor products of Banach modules
Abstract
We study injective and projective tensor products of measurable Banach bundles. More precisely, given two separable measurable Banach bundles , defined over a probability space , we construct two measurable Banach bundles and over such that and , where is the map assigning to a measurable Banach bundle its space of -sections, while and denote the injective and projective tensor…
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