The generalized west decomposition of operators and other compact perturbation problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space: (a) Every generalized Riesz operator has the generalized West decomposition; (b) Every operator makes strong Stampfli theorem true; (c) Every operator has Apostol's compact correction.