A completely hyperexpansive completion problem for weighted shifts on directed trees with one branching vertex

Let alpha = {alpha k}nk=0 be given a finite sequence of positive real numbers. The completely hyperexpan-sive completion problem seeks equivalence conditions for the existence of a completely hyperexpansive weighted shift W alpha such that alpha subset of alpha. Let T eta,kappa be a directed tree consisting of one branching vertex, eta branches and a trunk of length kappa, and let T eta,kappa,p be a subtree of T eta,kappa whose members consist of the p-generation family from branching vertex. Suppose S lambda is the weighted shift acting on the tree T eta,kappa. This object S lambda on the tree T eta,kappa has been applied to the several topics. Recently, Exner-Jung-Stochel-Yun studied the subnormal com-pletion problem for weighted shifts on T eta,kappa in 2018. In this paper we discuss the completely hyperexpansive completion problem for weighted shifts on T eta,kappa as a counterpart of the subnormal completion problem for S lambda.