In this short note, we establish a connection between the algebraic multiplicity of eigenvalues of compact integral operators and the simplicity of zeros of a class of the Mittag–Leffler functions $E_{\alpha ,\alpha }(z)$ and $E_{\alpha ,2}(z)$ for $1<\alpha <2$. Although these are two seemingly unrelated concepts in mathematics, our approach provides a functional‑analytic criterion for determining the simplicity of zeros in this class of Mittag–Leffler functions.