Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39120130301On the relations between the point spectrum of A and invertibility of I + f(A)B97106239ENH.LarkiIslamic Azad University, Parand BranchA.RiaziAmirkabir University of TechnologyJournal Article20110426Let A be a bounded linear operator on a Banach space X. We <br />investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function <br />f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an <br />operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some <br />conditions in this paper.http://bims.iranjournals.ir/article_239_aa94bb32deb5aba560c323c06fd34102.pdf