Endomorphisms of Pointwise Lipschitz Algebras
© 2020, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. Let (X, d) be a compact metric space. Then, the normed algebra of pointwise Lipschitz functions on X is denoted by Lip pw(X, d). We study and characterize the completeness of these algebras and obtain a necessary...
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| 格式: | 雜誌 |
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2020
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| 在線閱讀: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85086710874&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70727 |
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| 總結: | © 2020, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. Let (X, d) be a compact metric space. Then, the normed algebra of pointwise Lipschitz functions on X is denoted by Lip pw(X, d). We study and characterize the completeness of these algebras and obtain a necessary and sufficient condition for such an algebra to be complete. We then investigate the endomorphisms of Lip pw(X, d) by considering their associated self-maps. A necessary and sufficient condition is given for these operators to be compact. Moreover, we discuss relations between Lip pw(X, d) and other normed function algebras. |
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