  Recently, the propagation of information through quantum many-body systems,
developed to study quantum chaos, have found many application from black holes
to disordered spin systems. Among other quantitative tools, Krylov complexity
has been explored as a diagnostic tool for information scrambling in quantum
many-body systems. We introduce a universal limit to the growth of the Krylov
complexity in dissipative open quantum systems by utilizing the uncertainty
relation for non-hermitian operators. We also present the analytical results of
Krylov complexity for characteristic behavior of Lanczos coefficients in
dissipative systems. The validity of these results are demonstrated by explicit
study of transverse-field Ising model under dissipative effects.
