Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T06:33:46.005Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 January 2007

A. BOURHIM  and
V. G. MILLER
A. BOURHIM
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec (Québec), CanadaG1K 7P4 e-mail: bourhim@mat.ulaval.ca
V. G. MILLER
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA e-mail: vivien@math.msstate.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.

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

Keywords

Primary 47B37Secondary 47A1047A11
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 99 - 104
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Aiena, P. and Monsalve, O., Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435–448.CrossRefGoogle Scholar
2.Albrecht, E., Eschmeier, J. and Neumann, M. M., Some topics in the theory of decomposable operators, Oper. Theory Adv. Appl. 17 (1986), 15–34.Google Scholar
3.Aupetit, B. and Drissi, D., {Local spectrum and subharmonicity}, Proc. Edinburgh Math. Soc. (2) 39 (1996), 571–579.CrossRefGoogle Scholar
4.Bourhim, A., On the local spectral properties of weighted shift operators, Studia Math. 163 (2004), 141–69.CrossRefGoogle Scholar
5.Duggal, B. P., Tensor products of opertors-strong stability and p-hyponormality, Glasgow Math. J. 42 (2000), 371–381.CrossRefGoogle Scholar
6.Laursen, K. B. and Neumann, M. M., An introduction to local spectral theory, London Mathematical Society Monograph New Series No. 20 (Oxford University Press).CrossRefGoogle Scholar
7.Mbekhta, M., Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621–631.Google Scholar
8.Miller, T. L., Miller, V. G. and Neumann, M. M., Local spectral properties of weighted shifts, J. Operator Theory 51 (2004), 171–88.Google Scholar
9.Miller, T. L. and Neumann, M. M., The single-valued extension property for sums and products of commuting operators, Czechoslovak Math. J. 52 (127) (2002), no. 3, 635–642.CrossRefGoogle Scholar
10.Saito, T., Hyponormal operators and related topics, Lecture Notes in Mathematics, vol. 247 (Springer-Verlag, 1971).Google Scholar
11.Stochel, J., Seminormality of operators from their tensor products, Proc. Amer. Math. Soc. 124 (1996), 435–440.CrossRefGoogle Scholar
12.Tanahashi, K. and Chō, M., Tensor products of log-hyponormal and of class A(s,t) operators, Glasgow. Math. J. 46 (2004), 91–95.CrossRefGoogle Scholar