Let ๐ be a Banach *-algebra. By ๐ฎ๐ we denote the set of all self-adjoint elements of ๐ and by ๐ช๐ we denote the set of those elements in ๐ which can be represented as finite real-linear combinations of mutually orthogonal projections. The main purpose of this paper is to prove the following result:
Suppose that