Abstract. We study decompositions of a Banach space operator $T$ in the form $T=K+Q$, where $K$ is compact (or meromorphic) and where the spectrum of $Q$ is contained in the set of all accumulation points of the spectrum of $T$. Many known decomposition results of this type are subsumed in our construction. We prove that every Hilbert space operator has the meromorphic decomposition, and obtain an improvement of a result of Laurie and Radjavi on the West decomposition of Riesz operators in a Banach space.

AMS Subject Classification (1991): 47A10, 47A65, 47B06, 47B99

Received August 21, 1996 and in revised form January 15, 1997. (Registered under 6109/2009.)