Geodesic
On the Definition of C*-Algebras II
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 664-681

Voir la notice de l'article provenant de la source Cambridge University Press

The theory of noncommutative involutive Banach algebras (briefly Banach *-algebras) owes its origin to Gelfand and Naimark, who proved in 1943 the fundamental representation theorem that a Banach *-algebra with C*-condition (C*) is *-isomorphic and isometric to a norm-closed self-adjoint subalgebra of all bounded operators on a suitable Hilbert space.At the same time they conjectured that the C*-condition can be replaced by the B*-condition. (B*) In other words any B*-algebra is actually a C*-algebra. This was shown by Glimm and Kadison [5] in 1960. 
Magyar, Zoltán; Sebestyén, Zoltán. On the Definition of C*-Algebras II. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 664-681. doi: 10.4153/CJM-1985-035-7
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