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.

单词	TopologicallyIrreducibleRepresentationsAreAlgebricallyIrreducibleForCalgebras
释义	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.
随便看	LeviPseudoconvex Levi pseudoconvex LevisTheorem Levi’s theorem LevyCollapse Levy collapse LevyDesplanquesTheorem Levy-Desplanques theorem LevyMartingaleCharacterization Levy martingale characterization LevyProcess Levy process LevyProcess1 LevysConjecture Levy’s conjecture LewisCarroll Lewis Carroll LewyExtensionTheorem Lewy extension theorem LewyHypersurface Lewy hypersurface LexicographicOrder lexicographic order LeylandNumber Leyland number

topologically irreducible representations are algebrically irreducible for C*-algebras

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