THEORY OF SPECTRAL DECOMPOSITIONS WITH RESPECT TO THE IDENTITY FOR CLOSED OPERATORS

摘要

＜正＞ In this paper,the auther discusses some properties of closed operators acting on aBanach space with the spectral decomposition property with respect to the identity（abbrev.SDI）.First,some equivalent conditions are given for a closed operator T to have the SDI.Next,for every hyperinvariant subspace Y of T with the SDI,it is proved that thecoinduced operator=T/Y has the SDI.Finally,properties of maximal nets of hyperinva-riant subspaces are discussed.