States of a C* algebra

Things to remember Every C* homomorphism is a bounded linear map which preserve multiplication and involution. Every C* algebra is a Banach algebra, and therefore also a Banach space under the norm. Every * homomorphism from C* algebra to the set of complex numbers is a linear functional of this Banach space. Every * homomorphism between C* algebras are norm decreasing. (Thm 2.1.7, Murphy) Hence every multiplicative * linear functional of this C* algebra is in the closed unit ball of the dual space of the Banach space....

September 25, 2023 ยท Joel Sleeba