Category:Representations of C*-Algebras

This category contains results about Representations of C*-Algebras.
Definitions specific to this category can be found in Definitions/Representations of C*-Algebras.

Let $\struct {A, \ast, \norm {\, \cdot \,} }$ be a $\text C^\ast$-algebra.

Let $\struct {\HH, \innerprod \cdot \cdot}$ be a Hilbert space over $\C$.

Let $\map B \HH$ be the space of linear operators on $\HH$, considered as a $\text C^\ast$-algebra.

Let $\pi : A \to \map B \HH$ be a $\ast$-algebra homomorphism.

In the case of $A$ unital with identity element ${\mathbf 1}_A$, take $\map \pi { {\mathbf 1}_A} = I_{\map B \HH}$.

We call $\tuple {\pi, \HH}$ a representation of $\struct {A, \ast, \norm {\, \cdot \,} }$.