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

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

Contents Full-Text PDF