On the weak decomposition property $(\delta _w)$
Volume 167 / 2005
                    
                    
                        Studia Mathematica 167 (2005), 17-28                    
                                        
                        MSC: Primary 47A10, 47A11; Secondary 47B40.                    
                                        
                        DOI: 10.4064/sm167-1-2                    
                                    
                                                Abstract
We study a new class of bounded linear operators which strictly contains the class of bounded linear operators with the decomposition property ($\delta $) or the weak spectral decomposition property (weak-SDP). We treat general local spectral properties for operators in this class and compare them with the case of operators with $(\delta )$.