Irreducible subalgebras of quasi-normed operator ideals (Q1297961)

It is known that the only irreducible \(C_p\)-closed subalgebra of \(C_p\) is \(C_p\) itself. A generalization of this theorem is established and some extensions of recent reducibility results are obtained based on this generalization. We then apply these extensions to derive some decomposability results concerning semigroups of compact quasinilpotent positive operators on Banach lattices.