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

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve Freelancer DeepDyve Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations