Document Type: Research Paper
Islamic Azad University, Parand Branch
Amirkabir University of Technology
Let A be a bounded linear operator on a Banach space X. We
investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function
f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an
operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some
conditions in this paper.