Translator Disclaimer
June 2009 Peripheral Multiplicativity of Maps on Uniformly Closed Algebras of Continuous Functions Which Vanish at Infinity
Osamu HATORI, Takeshi MIURA, Hirokazu OKA, Hiroyuki TAKAGI
Tokyo J. Math. 32(1): 91-104 (June 2009). DOI: 10.3836/tjm/1249648411

Abstract

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.

Citation

Download Citation

Osamu HATORI. Takeshi MIURA. Hirokazu OKA. Hiroyuki TAKAGI. "Peripheral Multiplicativity of Maps on Uniformly Closed Algebras of Continuous Functions Which Vanish at Infinity." Tokyo J. Math. 32 (1) 91 - 104, June 2009. https://doi.org/10.3836/tjm/1249648411

Information

Published: June 2009
First available in Project Euclid: 7 August 2009

zbMATH: 1201.46046
MathSciNet: MR2541156
Digital Object Identifier: 10.3836/tjm/1249648411

Subjects:
Primary: 46J10

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.32 • No. 1 • June 2009
Back to Top