In mathematics, multipliers and centralizers are algebraic objects in the study of Banach spaces.
Let (X, ‖·‖) be a Banach space over a field K (either the real or complex numbers), and let Ext(X) be the set of extreme points of the closed unit ball of the continuous dual space X∗.
That is, there exists a function aT : Ext(X) → K such that making
the eigenvalue corresponding to p. Given two multipliers S and T on X, S is said to be an adjoint for T if i.e. aS agrees with aT in the real case, and with the complex conjugate of aT in the complex case.
The centralizer (or commutant) of X, denoted Z(X), is the set of all multipliers on X for which an adjoint exists.