From Wikipedia, the free encyclopedia
- (x + y)* = x* + y* for all x, y in A.
- for every λ in C and every x in A; here, denotes the complex conjugate of λ.
- (xy)* = y* x* for all x, y in A.
- (x*)* = x for all x in A.
In most natural examples, one also has that the involution is isometric, i.e.
- ||x*|| = ||x||,