Research Article

THE SINGLE-VALUED EXTENSION PROPERTY IS NOT PRESERVED UNDER SUMS AND PRODUCTS OF COMMUTING OPERATORS

A. BOURHIMa1 and V. G. MILLERa2

a1 Département de Mathématiques et de Statistique, Université Laval, Québec (Québec), Canada G1K 7P4 e-mail: bourhim@mat.ulaval.ca

a2 Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA e-mail: vivien@math.msstate.edu

Abstract.

We show that the sum and the product of two commuting operators with the single-valued extension property need not inherit this property.

(Received March 17 2006)

(Revised August 21 2006)

(Accepted August 03 2006)

Key Words:

  • Primary 47B37;
  • Secondary 47A10;
  • 47A11

Footnotes

The first author was supported by a CRM-ISM postdoctoral fellowship. The authors thank T. J. Ransford and T. L. Miller for useful comments and sincere encouragement.