Rocky Mountain Journal of Mathematics

A construction of a BSE-algebra of type I which is isomorphic to no $\rm C^*$-algebras

Jyunji Inoue and Sin-Ei Takahasi

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In this note, we construct a BSE-algebra of type I which is isomorphic to no C$^*$-algebras. This affirmatively solves the problem posed by Takahasi and Hatori, ``is there a BSE-algebra of type I isomorphic to no C$^*$-algebras?''

Article information

Rocky Mountain J. Math., Volume 47, Number 8 (2017), 2693-2697.

First available in Project Euclid: 3 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 46J40: Structure, classification of commutative topological algebras

BSE-algebra Segal algebra C$^*$-algebra Banach algebra


Inoue, Jyunji; Takahasi, Sin-Ei. A construction of a BSE-algebra of type I which is isomorphic to no $\rm C^*$-algebras. Rocky Mountain J. Math. 47 (2017), no. 8, 2693--2697. doi:10.1216/RMJ-2017-47-8-2693.

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