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), 565-576

MSC (1991):
Primary 47B20, 47B37; Secondary 47-04, 47A57, 15A57

Published electronically:
June 22, 2001

MathSciNet review:
1862138

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Abstract | References | Similar Articles | 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 rank-one perturbation of the recursive weight sequence , then subnormality and -hyponormality for eventually coincide. We then examine a converse--an ``extremality" problem: Let be a canonical rank-one 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 440-746, Korea

Email:
wylee@yurim.skku.ac.kr

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06079-8

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 first-named author was partially supported by NSF research grants DMS-9401455 and DMS-9800931.

The work of the second-named author was partially supported by KOSEF, research grant 2000-1-10100-002-3

The work of the third-named author was partially supported by the Brain Korea 21 Project.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society