Drazin invertibility of the diagonal of an operator

Abstract

In this article we will give relation between ascent and descent of a Banach space operator T and its diagonal (i.e. its restriction A to an invariant subspace and the induced quotient mapping B). This result is then applied to describe Drazin invertibility of one of these three operators using Drazin invertibility of the other two operators. It is proved that the operator T is meromorphic if and only if A and B are meromorphic.

Keywords:

• invariant subspace
• Drazin inverse
• ascent and descent

AMS Subject Classifications:

• Primary 47A10
• 47A15
• Secondary 47A05
• 15A29