Bulletin of the Belgian Mathematical Society - Simon Stevin

A Banach-Stone Theorem for completely regular spaces

Hamid Reza Shatery and Jafar Zafarani

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Abstract

In this paper, we study some Banach algebras with this property that each linear isometry between them induces a Banach algebra isometry. We obtain a Banach-Stone type theorem between Baire functions defined on completely regular spaces. As a consequence, a similar result for the space of continuous functions is deduced.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 555-564.

Dates
First available in Project Euclid: 28 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1190994218

Digital Object Identifier
doi:10.36045/bbms/1190994218

Mathematical Reviews number (MathSciNet)
MR2387054

Zentralblatt MATH identifier
1143.46004

Subjects
Primary: 46B04: Isometric theory of Banach spaces 46E15: Banach spaces of continuous, differentiable or analytic functions 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
Banach algebras Completely regular spaces Banach-Stone theorem Baire functions Borel functions

Citation

Shatery, Hamid Reza; Zafarani, Jafar. A Banach-Stone Theorem for completely regular spaces. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 555--564. doi:10.36045/bbms/1190994218. https://projecteuclid.org/euclid.bbms/1190994218


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