Extensions and extremality of recursively generated weighted shifts
Authors:
Raúl E. Curto, Il Bong Jung and Woo Young Lee
Journal:
Proc. Amer. Math. Soc. 130 (2002), 565576
MSC (1991):
Primary 47B20, 47B37; Secondary 4704, 47A57, 15A57
Published electronically:
June 22, 2001
MathSciNet review:
1862138
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Given an step extension of a recursively generated weight sequence , and if denotes the associated unilateral weighted shift, we prove that
In particular, the subnormality of an extension of a recursively generated weighted shift is independent of its length if the length is bigger than 1. As a consequence we see that if is a canonical rankone perturbation of the recursive weight sequence , then subnormality and hyponormality for eventually coincide. We then examine a conversean ``extremality" problem: Let be a canonical rankone perturbation of a weight sequence and assume that hyponormality and hyponormality for coincide. We show that is recursively generated, i.e., is recursive subnormal.
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Additional Information
Raúl E. Curto
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
curto@math.uiowa.edu
Il Bong Jung
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea
Email:
ibjung@bh.kyungpook.ac.kr
Woo Young Lee
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440746, Korea
Email:
wylee@yurim.skku.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002993901060798
PII:
S 00029939(01)060798
Keywords:
Extensions of weighted shifts,
recursively generated shifts,
$k$hyponormality
Received by editor(s):
July 14, 2000
Published electronically:
June 22, 2001
Additional Notes:
The work of the firstnamed author was partially supported by NSF research grants DMS9401455 and DMS9800931.
The work of the secondnamed author was partially supported by KOSEF, research grant 20001101000023
The work of the thirdnamed author was partially supported by the Brain Korea 21 Project.
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2001 American Mathematical Society
