PERTURBATION OF THE WIGNER EQUATION IN INNER PRODUCT C* -MODULES

. Let ช be a C* -subalgebra of a von Neumann algebra B Let M and N be inner product modules over ช and B, respectively. Under some assumptions we show that for each mapping f : M® N satisfying || |áf(x), f(y)ñ| − |áx, yñ| || j(x, y) (x, y ϵ M), where j is a control function, there exists a solution I : M ® N of the Wigner equation |áI(x), I(y)ñ| = |áx, yñ| (x, y ϵ M) such that ||f(x) − I(x)||≤ Ö j (x, x) (x ϵ M).

کلیدواژه ها:

Wigner equation ، inner product C -module ، von Neumann algebra ، stability