For a C*-algebra A let M(A) denote the two-sided multipliers of A in its enveloping von Neumann algebra. A complete description of M(A) is given in the case where the spectrum of A is Hausdorff. The formula M(A ⊗α B) = M(A) ⊗α M(B) is discussed and examples are given where M(A) A is non-simple even though A is simple and separable. As a generalization of Tietze's Extension Theorem it is shown that a multiplier of a quotient of A is the image of an element from M(A), if A is separable. Finally, deriving algebras and thin operators and their relations to multipliers are discussed. © 1973.
Akemann, C. A., Pedersen, G. K., & Tomiyama, J. (1973). Multipliers of C*-algebras. Journal of Functional Analysis, 13(3), 277–301. https://doi.org/10.1016/0022-1236(73)90036-0