Let with a infinite dimensional, separable Hilbert space. Let be an orthonormal basis for . Let be an operator in defined by
set now show that the following map is a *-isomorphism (bijective *-homomorphism)
Let with a infinite dimensional, separable Hilbert space. Let be an orthonormal basis for . Let be an operator in defined by
set now show that the following map is a *-isomorphism (bijective *-homomorphism)