Title

A Subnormal Completion Problem for Weighted Shifts on Directed Trees

Publication Date

11-18-2018

Description

Given a directed tree and a collection of weights on a subtree, the subnormal completion problem is to determine whether the weights may be completed to the weights of an injective, bounded, subnormal weighted shift on the Hilbert space arising from the full tree. We study this problem (which generalizes significantly the classical subnormal completion problem for weighted shifts) both from a measure-theoretic point of view and in terms of initial data, for various classes of trees with a single branching point. We give several characterizations of when such a completion is possible. Considered also are connections with Stieltjes moment sequences, flatness of a completion, completions in which the resulting measures may be taken to be finitely atomic, and we provide a result showing that in certain circumstances the present completion problem is equivalent to a related classical completion problem.

Journal

Integral Equations and Operator Theory

Volume

90

Department

Mathematics

DOI

https://doi.org/10.1007/s00020-018-2496-9

This document is currently not available here.

Share

COinS