Let A be a C^*-algebra. An element a element A is called positive if a = a* and s p(a)⊆ℜ^+, or equivalently if there exists an element b element A such that a = b b^*. For example, the positive elements of the C^*-algebra of complex numbers are the nonnegative real numbers. The set of all positive elements of A denoted by A_+ is called the positive part of A.