# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

# Real-Multilinear Isometries on Function Algebras

, Volume 72 (2) – Feb 25, 2017
18 pages

/lp/springer_journal/real-multilinear-isometries-on-function-algebras-GUsxxg0B76
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0660-1
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Results in MathematicsSpringer Journals

Published: Feb 25, 2017

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