nLab star-representation

Idea

For $(\mathcal{A}, \ast)$ a star-algebra and $\mathcal{H}$ a Hilbert space, a star-representation of $(\mathcal{A},\ast)$ on $\mathcal{H}$ is a homomorphism of star algebras from $\mathcal{A}$ to linear operators on (a dense subspace of) $\mathcal{H}$.

Related concepts

• representation of a C-star-algebra

• GNS construction

References

• Igor Khavkine, Valter Moretti, def. 7 in Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction, Chapter 5 in Romeo Brunetti et al. (eds.) Advances in Algebraic Quantum Field Theory, , Springer, 2015