A Note on Commutative Gelfand Theory for Real Banach Algebras

• Takahashi Sin-Ei

• Miura Takeshi

• Hatori Osamu

Abstract

Pfaffenberger and Phillips [2] consider a real and unital case of the classical commutative Gelfand theorem and obtain two representation theorems. One is to represent a unital real commutative Banach algebra A as an algebra of continuous functions on the unital homomorphism space ΦA. The other is to represent A as an algebra of continuous sections on the maximal ideal space MA. In this note, we point out that similar theorems for non-unital case hold and show that two representation theorems are essentially identical.

Journal

• Mathematical Journal of Okayama University

  Mathematical Journal of Okayama University 46 (1), 121-130, 2004-01

  Department of Mathematics, Faculty of Science, Okayama University

Keywords

• real commutative Banach algebras
• real algebra homomorphisms
• commutative Gelfand theory.

Details

• CRID: 1390290699601623680
• NII Article ID: 120002309904
• NII Book ID: AA00723502
• ISSN: 00301566
• DOI: 10.18926/mjou/33926
• Web Site: https://ousar.lib.okayama-u.ac.jp/33926
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
  • KAKEN