## Rocky Mountain Journal of Mathematics

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

#### Abstract

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

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

Dates
First available in Project Euclid: 3 February 2018

https://projecteuclid.org/euclid.rmjm/1517648606

Digital Object Identifier
doi:10.1216/RMJ-2017-47-8-2693

Mathematical Reviews number (MathSciNet)
MR3760313

Zentralblatt MATH identifier
06840995

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1517648606

#### References

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• S.-E. Takahasi and O. Hatori, Commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein type-theorem, Proc. Amer. Math. Soc. 110 (1990), 149–158.