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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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References
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1.Aiena P. and Monsalve O., Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435448.
2.Albrecht E., Eschmeier J. and Neumann M. M., Some topics in the theory of decomposable operators, Oper. Theory Adv. Appl. 17 (1986), 1534.
3.Aupetit B. and Drissi D., {Local spectrum and subharmonicity}, Proc. Edinburgh Math. Soc. (2) 39 (1996), 571579.
4.Bourhim A., On the local spectral properties of weighted shift operators, Studia Math. 163 (2004), 14169.
5.Duggal B. P., Tensor products of opertors-strong stability and p-hyponormality, Glasgow Math. J. 42 (2000), 371381.
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).
7.Mbekhta M., Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621631.
8.Miller T. L., Miller V. G. and Neumann M. M., Local spectral properties of weighted shifts, J. Operator Theory 51 (2004), 17188.
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, 635642.
10.Saito T., Hyponormal operators and related topics, Lecture Notes in Mathematics, vol. 247 (Springer-Verlag, 1971).
11.Stochel J., Seminormality of operators from their tensor products, Proc. Amer. Math. Soc. 124 (1996), 435440.
12.Tanahashi K. and Chō M., Tensor products of log-hyponormal and of class A(s,t) operators, Glasgow. Math. J. 46 (2004), 9195.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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