On the relations between the point spectrum of A and invertibility of I + f(A)B
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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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Journal title
volume 39 issue 1
pages 97- 106
publication date 2013-03-01
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