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On the Definition of C*-Algebras II

Published online by Cambridge University Press:  20 November 2018

Zoltán Magyar  and
Zoltán Sebestyén
Zoltán Magyar
Affiliation:
Eötvös Lorand University, Budapest, Hungary
Zoltán Sebestyén
Affiliation:
Eötvös Lorand University, Budapest, Hungary
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 4 , 01 August 1985 , pp. 664 - 681
Copyright
Copyright © Canadian Mathematical Society 1985

References

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