Hyers-Ulam stability of some linear operators on a Hilbert space

Abstract

Suppose that $T$ is a bounded  operator from a Hilbert space $H$ into $H$. In this paper, for an injective  cohyponormal or complex symmetric operator $T$, we find a necessary and sufficient condition for $T$ to have the  Hyers-Ulam stability. Moreover, when $T$ is injective, we find  necessary and sufficient conditions for $T^{\ast}T$ to have the Hyers-Ulam stability.