Abstract
The notion of tensor product of a family (A i ) i εI of Banach algebras is generalized to the case whenI is a topological space; in this case\(\widehat \otimes \) A i is generated by some elements ⊗x i , the family (x i ) being subjected to certain conditions: for instance the functioni → ‖x i ‖ must be continuous. This notion is applied to Quantum Field Theory in the following sense: certain algebras of observables can be considered as continuous tensor products of simpler ones, namely of algebras of observables with one degree of freedom.
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Guichardet, A. Produits tensoriels continus d'espaces et d'algèbres de Banach. Commun.Math. Phys. 5, 262–287 (1967). https://doi.org/10.1007/BF01646479
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DOI: https://doi.org/10.1007/BF01646479