Definition 3

A Banach involutive algebra A such that $\|x\|^2=\|x^*x\|$ for every $x\in A$ is called a stellar algebra.

If A and B are stellar algebras, a morphism, or morphism of stellar algebras, from A into B is a morphism of involutive algebras from A into B. An isomorphism from A onto B is an isomorphism of involutive algebras from A onto B.

Some authors speak of a "$C^*$-algebra".

Let A be a stellar algebra. A stellar subalgebra of A is a closed involutive subalgebra of A.