A special case from particular importance is the case where is a
complete normed *-algebra. This algebra satisfies the C*-identity () and is called a
C*-algebra.
If is a normal element of a C*-algebra , then for every
continuous function on the spectrum the continuous functional calculus defines an unitary element , if .[2]
Blackadar, Bruce (2006). Operator Algebras. Theory of C*-Algebras and von Neumann Algebras. Berlin/Heidelberg: Springer. pp. 57, 63.
ISBN3-540-28486-9.
Dixmier, Jacques (1977). C*-algebras. Translated by Jellett, Francis. Amsterdam/New York/Oxford: North-Holland.
ISBN0-7204-0762-1. English translation of Les C*-algèbres et leurs représentations (in French). Gauthier-Villars. 1969.
Kadison, Richard V.; Ringrose, John R. (1983). Fundamentals of the Theory of Operator Algebras. Volume 1 Elementary Theory. New York/London: Academic Press.
ISBN0-12-393301-3.
A special case from particular importance is the case where is a
complete normed *-algebra. This algebra satisfies the C*-identity () and is called a
C*-algebra.
If is a normal element of a C*-algebra , then for every
continuous function on the spectrum the continuous functional calculus defines an unitary element , if .[2]
Blackadar, Bruce (2006). Operator Algebras. Theory of C*-Algebras and von Neumann Algebras. Berlin/Heidelberg: Springer. pp. 57, 63.
ISBN3-540-28486-9.
Dixmier, Jacques (1977). C*-algebras. Translated by Jellett, Francis. Amsterdam/New York/Oxford: North-Holland.
ISBN0-7204-0762-1. English translation of Les C*-algèbres et leurs représentations (in French). Gauthier-Villars. 1969.
Kadison, Richard V.; Ringrose, John R. (1983). Fundamentals of the Theory of Operator Algebras. Volume 1 Elementary Theory. New York/London: Academic Press.
ISBN0-12-393301-3.