Generalized eigenspace is finite

Can anyone give a reference or a proof to show the generalized eigenspace corresponding to a non zero eigenvalue of a compact operator defined on a Banach space is finite dimensional? I already saw the answer when the operator defined on a Hilbert space.

Thanks!

• What do you mean when you write that a generalized eigenspace is finite? There are at least a couple of things that could mean. – DisintegratingByParts Jun 17 '17 at 15:44
• I'm sorry. It should be finite dimensional. thanks. – Mathsira Jun 17 '17 at 15:47