Backward 3-step extensions of recursively generated weighted shifts: a range of quadratic hyponormality

Authors

  • G. R. Exner Bucknell University
  • I. B. Jung Kyungpook National University
  • M. R. Lee Kyungpook National University
  • S. H. Park Kyungpook National University

Keywords:

weighted shifts, quadratic hyponormality, positive quadratic hyponormality, subnormal completion

Abstract

Let \(\alpha:1,1,\sqrt{x},(\sqrt{u},\sqrt{v},\sqrt{w})^{\wedge }\) be a backward \(3\)-step extension of a recursively generated weighted sequence of positive real numbers with \(1\leq x\leq u\leq v\leq w\) and let \(W_{\alpha }\) be the associated weighted shift with weight sequence \(\alpha \). The set of positive real numbers \(x\) such that \(W_{\alpha }\) is quadratically hyponormal for some \(u,v\) and \(w\), is described, solving an open problem due to Curto and Jung [‘Quadratically hyponormal weighted shifts with two equal weights’, Integr. Equ. Oper. Theory \(37\) (2000), 208–231]. DOI: 10.1017/S0004972713000920

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles
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