The article concerned with the problem of regarding Lyapunov exponents of a random difference equation as the spectrum of an operator acting on a suitable space. Let $L$ be the set of all sequences of random variables having finite $p^{th}$ moments for some $p$ small, endowed with a certain topology. From the difference equation $X(n+1)=A(n)X(n)$; $X(0)=x\in R^d$, where $(A(n),n\in Z)$ is an i.i.d. sequence of random variables, we construct an operator $T$ acting on the space $L$. It is proved that the spectrum of the operator $T$ is contained in the set of sample Lyapunov exponents of this random dynamical system.