T. K. Carne, Andrew M. Tonge
Abstract
When A1 and A2 are Banach algebras, their algebraic tensor product A1 ⊗ A2 has a natural multiplication. In this paper we investigate when the condition that A1 and A2 are ℒp-spaces constrains this multiplication to extend to the injective tensor product A1 A2, making it a Banach algebra.
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When A1 and A2 are Banach algebras, their algebraic tensor product A1 ⊗ A2 has a natural multiplication. In this paper we investigate when the condition that A1 and A2 are ℒp-spaces constrains this multiplication to extend to the injective tensor product A1 A2, making it a Banach algebra.
Key concepts: Tensor product, Tensor product of Hilbert spaces, Injective function, Tensor product of modules, Tensor product of algebras, Multiplication (music), Mathematics, Tensor algebra