A generalization of the punctured neighborhood theorem

Lee, Woo Young

doi:10.1090/S0002-9939-1993-1113645-7

A generalization of the punctured neighborhood theorem
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Proc. Amer. Math. Soc. 117 (1993), 107-109 Request permission

Abstract:

If $T \in \mathcal {L}(X)$ is regular on a Banach space $X$, with finite- dimensional intersection ${T^{ - 1}}(0) \cap T(X)$, and if $S,\;S’$ are invertible, commute with $T$ and have sufficiently small norm, then $\dim {(T - S’)^{ - 1}}(0) = \dim {(T - S)^{ - 1}}(0)$ and $\dim X/(T - S’)X = \dim X/(T - S)X$.

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