Star-algebra ($(ab{)}^{\ast }=b^{\ast }{a}^{\ast },(a^{\ast }{)}^{\ast }=a$)

A complex associative algebra with a conjugate-linear involution satisfying the displayed product-reversal identities. An operator algebra closed under the Hilbert-space adjoint is a star-algebra. A C-star algebra additionally has a complete norm with $\Vert a^{\ast }a\Vert =\Vert a{\Vert }^2$.