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.
Larki, H., & Riazi, A. (2013). On the relations between the point spectrum of A and invertibility of I + f(A)B. Bulletin of the Iranian Mathematical Society, 39(1), 97-106.
MLA
Larki, H., & Riazi, A. "On the relations between the point spectrum of A and invertibility of I + f(A)B", Bulletin of the Iranian Mathematical Society, 39, 1, 2013, 97-106.
HARVARD
Larki H., Riazi A. (2013). 'On the relations between the point spectrum of A and invertibility of I + f(A)B', Bulletin of the Iranian Mathematical Society, 39(1), pp. 97-106.
CHICAGO
H. Larki & A. Riazi, "On the relations between the point spectrum of A and invertibility of I + f(A)B," Bulletin of the Iranian Mathematical Society, 39 1 (2013): 97-106,
VANCOUVER
Larki H., Riazi A. On the relations between the point spectrum of A and invertibility of I + f(A)B. BIMS. 2013;39(1):97-106.
