On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces

For linear differential operators with coefficients of class $C$ on $\mathbb R^n$, we prove theorems on the simultaneous invertibility and equivalence of spectra in the Lebesgue space $L^p$, Stepanov space $M^p$, and in a particular Banach space $V^p\subset L^p$, $p\ge 1$.