  We show that a Kurdyka-\L{}ojasiewicz (KL) inequality can be used as
regularity condition for Tikhonov regularization with linear operators in
Banach spaces. In fact, we prove the equivalence of a KL inequality and various
known regularity conditions (variational inequality, rate conditions, and
others) that are utilized for postulating smoothness conditions to obtain
convergence rates. Case examples of rate estimates for Tikhonov regularization
with source conditions or with conditional stability estimate illustrate the
theoretical result.
