Journal of Operator Theory

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

On the punctured neighbourhood theorem

Authors: Vladimir Muller
Author institution: Institute of Mathematics AVCR, Zitna 25, 115 67 Prague 1, Czech Republic

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 $z\mapsto\dim \ker T(z)/\Im S(z)$.

Keywords: Punctured neighbourhood theorem, complex of Banach spaces, analytic set

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