Kato decomposition of linear pencils
T. Kato [5] found an important property of semi-Fredholm pencils, now called the Kato decomposition. M. A. Kaashoek [3] introduced operators having the property P(S:k) as a generalization of semi-Fredholm operators. In this work, we study this class of operators. We show that it is characterized by a Kato-type decomposition. Other properties are also proved.