topologically irreducible representations are algebrically irreducible for $C^{*}$-algebras

Theorem - Every topologically irreducible representation (http://planetmath.org/BanachAlgebraRepresentation) of a $C^{*}$-algebra (http://planetmath.org/CAlgebra) is algebraically irreducible.

$Remark-$ It follows easily from the definition that algebraically irreducible of any Banach *-algebra are always topologically irreducible. The above theorem says that for $C^{*}$-algebras the converse is also true.

Title topologically irreducible representations are algebrically irreducible for $C^{*}$-algebras TopologicallyIrreducibleRepresentationsAreAlgebricallyIrreducibleForCalgebras 2013-03-22 17:27:47 2013-03-22 17:27:47 asteroid (17536) asteroid (17536) 5 asteroid (17536) Theorem msc 46L05