Ill-posed problems, C0-semigroups and the Showalter regularization

We consider linear operator equations Ax = y in Banach space, where −A generates a bounded C0-semigroup. If the range of A is not closed, this equation is ill-posed. It can be solved approximately by Showalter’s method, which is known for bounded linear operators in Hilbert space. We show convergence and estimate convergence rates in Banach space.  2004 Elsevier Inc. All rights reserved