CHARACTERISATIONS OF OPERATORS OF LOWER SEMI-FREDHOLM TYPE IN NORMED LINEAR SPACES

摘要

LetXandYbe normed linear spaces. A linear operatorT:D(T) #x2282;X#x2192;Yis called anF-operator if its adjointT#x2032;:D(T) #x2282;Y#x2032;#x2192;D(T)' is a#x3C6;+-operator, i.e. has closed range and finite dimensional-kernel. Characterisations of anF_-operatorTare obtained in the general case and in the case whenTis closable. Unbounded strictly cosingular operators are defined and shown to belong to the class ofF_ -admissible pertubations wheneverYis complete.