On the relations between the point spectrum of A and invertibility of I + f(A)B

Document Type: Research Paper

Authors

1 Islamic Azad University, Parand Branch

2 Amirkabir University of Technology

Abstract

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.

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