Real-Multilinear Isometries on Function Algebras

Real-Multilinear Isometries on Function Algebras Let $$A_1, \ldots , A_k$$ A 1 , … , A k be function algebras (or more generally, dense subspaces of uniformly closed function algebras) on locally compact Hausdorff spaces $$X_1, \ldots ,X_k$$ X 1 , … , X k , respectively, and let Y be a locally compact Hausdorff space. A k-real-linear map $$T:A_1\times \cdots \times A_k\longrightarrow C_0(Y)$$ T : A 1 × ⋯ × A k ⟶ C 0 ( Y ) is called a real-multilinear (or k-real-linear) isometry if $$\begin{aligned} \Vert T(f_1, \ldots , f_k)\Vert =\prod _{i=1}^{k} \Vert f_i\Vert \quad ((f_1, \ldots , f_k)\in A_1\times \cdots \times A_k), \end{aligned}$$ ‖ T ( f 1 , … , f k ) ‖ = ∏ i = 1 k ‖ f i ‖ ( ( f 1 , … , f k ) ∈ A 1 × ⋯ × A k ) , where $$\Vert \cdot \Vert $$ ‖ · ‖ denotes the supremum norm. In this paper we study such maps and obtain generalizations of basically all known results concerning multilinear and real-linear isometries on function algebras. Results in Mathematics Springer Journals

Real-Multilinear Isometries on Function Algebras

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Springer International Publishing
Copyright © 2017 by Springer International Publishing
Mathematics; Mathematics, general
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