Hostname: page-component-54dcc4c588-b5cpw Total loading time: 0 Render date: 2025-10-04T14:05:54.451Z Has data issue: false hasContentIssue false
  • English
  • Français

Moment sequences and backward extensions of subnormal weighted shifts

Part of: Special classes of linear operators Integral transforms, operational calculus

Published online by Cambridge University Press:  09 April 2009

Thomas Hoover ,
Il Bong Jung  and
Alan Lambert
Thomas Hoover
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822, USA e-mail: hoover@math.hawaii.edu
Il Bong Jung
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National UniversityTaegu 702-701Korea e-mail: ibjung@kyungpook.ac.kr
Alan Lambert
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, UNCC Station Charlotte, NC 28223USA e-mail: allamber@email.uncc.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we examine the relationships between a subnormal shift, the measure its moment sequence generates, and those of a large family of weighted shifts associated with the original shift. We examine the effects on subnormality of adding a new weight or changing a weight. We also obtain formulas for evaluating point mass at the origin for the measure associated with the shift. In addition, we examine the relationship between the measure associated with a subnormal shift and those of a family of shifts substantially different from the original shift.

Keywords

weighted shiftssubnormal operatorsmoment sequences

MSC classification

Secondary: 47B20: Subnormal operators, hyponormal operators, etc. 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 44A60: Moment problems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 27 - 36
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Curto, R., ‘Quadratically hyponormal weighted shifts’, Integral Equations Operator Theory 13 (1990), 49–66.CrossRefGoogle Scholar
[2]Embry, M., ‘A generalization of the Halmos-Bram criterion for subnormality’, Acta Sci. Math. (Szeged) 35 (1973), 61–64.Google Scholar
[3]Halmos, P., ‘Ten problems in Hilbert space’, Bull. Amer. Math. Soc. 76 (1970), 887–933.CrossRefGoogle Scholar
[4]Lambert, A., ‘Subnormality and weighted shifts’, J. London Math. Soc. 14 (1976), 476–480.CrossRefGoogle Scholar
[5]Shields, A., Weighted shift operators and analytic finction theory, Topics in Operator Theory, Math. Surveys 13 (Amer. Math. Soc., Providence, RI, 1974).Google Scholar