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 α:1,1,√x,(√u,√v,√w)∧ be a backward 3-step extension of a recursively generated weighted sequence of positive real numbers with 1≤x≤u≤v≤w and let Wα be the associated weighted shift with weight sequence α. The set of positive real numbers x such that Wα 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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