TY - JOUR ID - 239 TI - On the relations between the point spectrum of A and invertibility of I + f(A)B JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Larki, H. AU - Riazi, A. AD - Islamic Azad University, Parand Branch AD - Amirkabir University of Technology Y1 - 2013 PY - 2013 VL - 39 IS - 1 SP - 97 EP - 106 KW - point spectrum KW - rank-one operator KW - invariant subspaces DO - N2 - 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. UR - http://bims.iranjournals.ir/article_239.html L1 - http://bims.iranjournals.ir/article_239_aa94bb32deb5aba560c323c06fd34102.pdf ER -