Stability of Derivations on Hilbert $C^{\ast }$-Modules

Abstract

Consider the functional equation ${\mathcal{E}}_1(f)={\mathcal{E}}_2(f)(\mathcal{E})$ in a certain framework. We say a function $f_0$ is an approximate solution of $(\mathcal{E})$ if ${\mathcal{E}}_1(f_0)$ and ${\mathcal{E}}_2(f_0)$ are close in some sense. The stability problem is whether or not there is an exact solution of $(\mathcal{E})$ near $f_0$. In this paper, the stability of derivations on Hilbert $C^{\ast }$-modules is investigated in the spirit of Hyers--Ulam--Rassias.

9 pages, to appear in Contemp. Math (Amer. Math. soc.)

Cited by in corpus (2)

• Perturbation of the Wigner equation in inner product C*-modules
• Superstability of adjointable mappings on Hilbert $C^{\ast }$-modules