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

  • A. BOURHIM (a1) and V. G. MILLER (a2)
Abstract
Abstract.

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

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. P. Aiena and O. Monsalve , Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435448.

7. M. Mbekhta , Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621631.

3. B. Aupetit and D. Drissi , {Local spectrum and subharmonicity}, Proc. Edinburgh Math. Soc. (2) 39 (1996), 571579.

5. B. P. Duggal , Tensor products of opertors-strong stability and p-hyponormality, Glasgow Math. J. 42 (2000), 371381.

12. K. Tanahashi and M. Chō , Tensor products of log-hyponormal and of class A(s,t) operators, Glasgow. Math. J. 46 (2004), 9195.

4. A. Bourhim , On the local spectral properties of weighted shift operators, Studia Math. 163 (2004), 1 4169.

9. T. L. Miller and M. M. Neumann , The single-valued extension property for sums and products of commuting operators, Czechoslovak Math. J. 52 (127) (2002), no. 3, 635642.

11. J. Stochel , Seminormality of operators from their tensor products, Proc. Amer. Math. Soc. 124 (1996), 435440.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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