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# Journal of Operator Theory

Volume 43, Issue 1, Winter 2000  pp. 83-95.

On the punctured neighbourhood theorem

Summary:  Let $X,Y,Z$ be Banach spaces and $X\toind{S(z)} Y\toind{T(z)}Z$ an analytically dependent sequence of operators satisfying $T(z)S(z)=0$. We study the properties of the function $z\mapsto\dim \ker T(z)/\Im S(z)$.