# Closable Hankel operators and moment problems

## TL;DR

This paper revises previous claims about the conditions under which Hankel operators related to moment sequences are closable, showing that closability extends beyond the previously asserted criteria.

## Contribution

It corrects and extends Yafaev's 2016 results by establishing broader conditions for the closability of Hankel operators associated with moment sequences.

## Key findings

- Closability holds for all indeterminate moment sequences.
- Certain determinate sequences with finite index of determinacy also have closable Hankel operators.
- Yafaev's condition holds if {2n}{o(n)} for the moments.

## Abstract

In a paper from 2016 D. R. Yafaev considers Hankel operators associated with Hamburger moment sequences q_n and claims that the corresponding Hankel form is closable if and only if the moment sequence tends to 0. The claim is not correct, since we prove closability for any indeterminate moment sequence but also for certain determinate moment sequences corresponding to measures with finite index of determinacy. It is also established that Yafaev's result holds if the moments satisfy \root{2n}\of{q_{2n}}=o(n).