Equivalence of $K$-irreducibility concepts
Ivo Marek, Karel Žitný · Czech digital mathematics library · 1984
fhe equiTalence of Tarious concepts of irreducibility of positiTe operators in partially ordered Banach^spaces introduced by G. Frobenius (.Fr) f H. Geiringer (Ge) f Konig (Ko), H.H. Schaefer (Sc), I. Sawashima (Sa) f J^S.Yandergraft (VS) f V.Ya.Stecenko (St) and I. Marek and K. Zitny (MZ) is analyzed,, All the concepts considered are equiTalent if the dimension of the spaces under consideration is at least two.In onedimensional spaces these concepts split into two classes -the oriterion being a classification of the zero map as reducible ((MZ) f (Sa),(ScT) or irreducible (0?r),(Ge) f (Ko) f (St) f (TS)) t respectiTely.