In Laundau & Lifshitz Quantum Mechanics. Non-relativistic theory in $\S29$ a problem is given:
PROBLEM Average the tensor $n_in_k-\frac13\delta_{ik}$ (where $\mathbf{n}$ is a unit vector along the radius vector of a particle) over a state where the magnitude but not the direction of the vector $\mathbf{l}$ is given (i.e. $l_z$ is indeterminate).
The solution then starts with this (italics mine):
$\def\sc#1{\dosc#1\csod} \def\dosc#1#2\csod{{\rm #1{\small #2}}} \sc{SOLUTION.}$ The required mean value is an operator which can be expressed in terms of the operator $\mathbf{\hat l}$ alone. We seek it in the form
$$\overline{n_in_k}-\frac13\delta_{ik}=a[\hat l_i\hat l_k+\hat l_k\hat l_i-\frac23\delta_{ik}l(l+1)];$$
this is the most general symmetrical tensor of rank two with zero trace that can be formed from the components of $\mathbf{\hat l}$. ...
What confuses me is the italicized part: "mean value is an operator". As I understand, mean value in a given state $|\psi\rangle$ of a quantity $\kappa$ is given by
$$\overline\kappa=\langle\psi|\hat\kappa|\psi\rangle.$$
Here $\overline\kappa$ is not an operator, but $\hat\kappa$ is. Do L&L try to abbreviate some clearer phrase by their statement? Or do I understand something wrongly?