The spectrum of a Volterra composition operator
Lyubic conjectured that the Volterra composition operator \(Vf(t)=\int^{\phi (x)}_{0}f(t)dt\), \(\phi\) continuous, is quasinilpotent as an operator on C[0,1] iff \(\phi\) (x)\(\leq x\) for x in [0,1]. This conjecture is established and extended to V as an operator on \(L^ p[0,1]\).
scientific article; zbMATH DE number 4009147