Hostname: page-component-5447f9dfdb-lxcff Total loading time: 0 Render date: 2025-07-28T10:54:55.358Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of a Sparse Blaschke Product

Published online by Cambridge University Press:  20 November 2018

Carroll Guillory
Carroll Guillory*
Affiliation:
University of Southwestern Louisiana Lafayette, LA 70504
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.

We give a characterization of a sparse Blaschke product b in terms of the separation of support sets of its zeros in M(H∞ + C) and the structure of the nonanalytic points. We use this characterization to give a sufficient condition on an interpolating Blaschke product q to have the following property: there exists a non trivial Gleason part P on which q is nonzero and less than one.

Keywords

46J1546J20

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 385 - 390
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Browder, A., Introduction of Function Algebras, W. A. Benjamin, Inc., 1969.Google Scholar
2. Budde, P., Ph.D. Dissertation, Univ. of California, Berkeley, 1982.Google Scholar
3. Guillory, C. J., Douglas Algebras of the Form H∞[q̄], to appear in the J. of Math. Anal.Google Scholar
4. Guillory, C. J., Izuchi, K. and Sarason, D., Interpolating Blaschke products and division in Douglas algebras, Proc. Royal Irish Adac. 84A (1984),l–7.Google Scholar
5. Izuchi, K., Zero sets of interpolating Blaschke products, to appear in the Pac. J. of Math.Google Scholar