2009年
Peripheral Multiplicativity of Maps on Uniformly Closed Algebras of Continuous Functions Which Vanish at Infinity
Tokyo Journal of Mathematics
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- 巻
- 32
- 号
- 1
- 開始ページ
- 91
- 終了ページ
- 104
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.3836/tjm/1249648411
We study maps between uniformly closed algebras of complex-valued continuous functions which vanish at infinity on locally compact Hausdorff spaces. Without assuming linearity nor multiplicativity on the maps we show that they are isometrical isomorphisms as Banach space operators if they satisfy that the peripheral range of the product of the images of any two elements coincides with the peripheral range of the product of those elements. Furthermore, if the underlying algebras contain approximate identities, then they are isometrically isomorphic as Banach algebras, which is a generalization of a recent result of Luttman and Tonev for the case of uniform algebras. On the other hand it is not the case without assuming the existence of approximate identities
An example is given. © 2009 International Academic Printing Co. Ltd. All rights reserved.
An example is given. © 2009 International Academic Printing Co. Ltd. All rights reserved.
- ID情報
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- DOI : 10.3836/tjm/1249648411
- ISSN : 0387-3870
- SCOPUS ID : 77957221544