B^*-algebra

A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* | = | x x^* y^* | = | (y x)^* x^* + y^* | = | (x + y)^* (c x)^* | = | c^_ x^*, where c^_ is the complex conjugate of c, and whose norm satisfies left double bracketing bar x x^* right double bracketing bar = ( left double bracketing bar x right double bracketing bar )^2.

K-theory | pre-C^*-algebra