Banach star-algebra
= Banach star-algebra
{c}
{title2=$(ab)^*=b^*a^*,\quad(a^*)^*=a$}
A <Banach star-algebra> is a complex <Banach algebra> equipped with a continuous <algebra involution>. Thus the involution is conjugate-linear, reverses products, and squares to the identity. Some conventions additionally require $\|a^*\|=\|a\|$; this is the isometric convention. In the unital case the involution fixes the unit. The <C-star identity> is a stronger additional condition. The algebra of continuous complex-valued functions on a <compact Hausdorff space>, with pointwise operations, <complex conjugation> and the <supremum norm>, satisfies both the isometric condition and the C-star identity.