: (the involution of the sum of x and y is equal to the sum of the involution of x with the involution of y) |
|
: (the involution of the product of x and y is equal to the product of the involution of x with the involution of y) |
: (the involution of the involution of x is equal to x) |
If the last property is omitted, we speak of a B*-algebra. |
: (the norm of the product of x and the involution of x is equal to the norm of x squared ) If the last property is omitted, we speak of a '''B*-algebra'''. |
* f(xy) = f(x)f(y) |
* f(xy) = f(x)f(y) for x and y in A (and x and y in B) : (the function applied to the product of x and y is equal to product of the function applied to x with the function applied to y ) |