Abstract. In this note we give conditions for the invertibility of a bounded linear operator $T$ defined on a Banach space $X$ such that $X$ decomposes into a (non direct) sum of two closed $T$-invariant subspaces.

DOI: 10.14232/actasm-015-534-x

AMS Subject Classification (1991): 47A10, 47A15,47A05, 15A29

Keyword(s): invariant subspace, spectrum of an operator

Received May 13, 2015, and in final form April 6, 2016. (Registered under 34/2015.)