C∗-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables.