Local Multipliers of C*-Algebras

The book delves into operator theory and the necessity of enlarging spaces to find solutions to operator equations. It highlights the Berberian-Quigley enlargement of Banach spaces, which transforms approximate eigenvectors into genuine ones. The discussion extends to C*-algebras, illustrating how they are often enlarged to their universal enveloping von Neumann algebras for richer properties. Notably, it covers the Kadison-Sakai theorem, demonstrating that derivations can become inner in the enlarged space, while addressing the limitations of algebraic transitions in certain cases.