  This paper develops a Tikhonov regularization theory for nonlinear ill-posed
operator equations in Banach spaces. As the main challenge, we consider the
so-called oversmoothing state in the sense that the Tikhonov penalization is
not able to capture the true solution regularity and leads to the infinite
penalty value in the solution. We establish a vast extension of the Hilbertian
convergence theory through the use of invertible sectorial operators from the
holomorphic functional calculus and the prominent theory of interpolation
scales in Banach spaces. Applications of the proposed theory involving
$\ell^1$, Bessel potential spaces, and Besov spaces are discussed.

Functional Analysis