Title

Weak Hamburger-type weighted shifts and their examples

Publication Date

2018

Journal

Journal of Mathematical Analysis and Applications

Volume

462

Issue

2

First Page

1357

Last Page

1380

Department

Mathematics

Abstract

Let Wα be a bounded weighted shift with weight sequence α={αn}∞n=0 and let γn=α20···α2n−1(n≥1) with γ0=1. The positivity of both of the infinite matrices (γi+j)0≤i,j<∞ and (γi+j+1)0≤i,j<∞ is a condition equivalent to subnormality of Wα. For a positive integer n, the positivity of (γi+j)0≤i, j<n defines property H(n) for Wα which is closely related to the flatness of α. As a study of the flatness property, the problem “describe weighted shifts Wα with property H(n) such that α1=α2” is considered. We solve this problem in the case of weighted shifts whose weight sequence has Bergmantail, and also in the case of shifts whose weight sequence is the backward extension of a Hamburger completion (α0,α1,α2)H. In addition, we discuss some examples to show the properties H(n), ̃H(n), and n-hyponormality are distinct.

DOI

https://doi.org/10.1016/j.jmaa.2018.02.045

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