Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
single-valued extension property; Dunford’s property $\mathrm (C)$; decomposable operators
single-valued extension property; Dunford’s property $\mathrm (C)$; decomposable operators
Summary:
It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property $\mathrm (C)$ have the single-valued extension property.
References:
[1] E. Albrecht and J. Eschmeier: Analytic functional models and local spectral theory. Proc. London Math. Soc. 75 (1997), 323–348. MR 1455859
[2] E. Albrecht, J. Eschmeier and M. M. Neumann: Some topics in the theory of decomposable operators. In: Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, Vol. 17, Birkhäuser Verlag, Basel, 1986, pp. 15–34. MR 0901056
[3] C. Apostol: Decomposable multiplication operators. Rev. Roumaine Math. Pures Appl. 17 (1972), 323–333. MR 0310665 | Zbl 0239.47013
[4] B. Aupetit and D. Drissi: Local spectrum and subharmonicity. In: Proc. Edinburgh Math. Soc. Vol. 39, 1996, pp. 571–579. MR 1417698
[5] I. Colojoară and C. Foiaş: Theory of Generalized Spectral Operators. Gordon and Breach, New York, 1968. MR 0394282
[6] J. Eschmeier: Spectral decompositions and decomposable multipliers. Manuscripta Math. 51 (1985), 201–224. DOI 10.1007/BF01168353 | MR 0788679 | Zbl 0578.47024
[7] J. Eschmeier, K. B. Laursen and M. M. Neumann: Multipliers with natural local spectra on commutative Banach algebras. J. Funct. Analysis 138 (1996), 273–294. MR 1395959
[8] R. Kantrowitz and M. M. Neumann: On certain Banach algebras of vector-valued functions. In: Function spaces, the second conference. Lecture Notes in Pure and Applied Math. Vol. 172, Marcel Dekker, New York, 1995, pp. 223–242. MR 1352233
[9] R. Lange and S. Wang: New Approaches in Spectral Decomposition. Contemp. Math. 128. Amer. Math. Soc., Providence, RI, 1992. MR 1162741
[10] K. B. Laursen and M. M. Neumann: Asymptotic intertwining and spectral inclusions on Banach spaces. Czechoslovak Math. J. 43(118) (1993), 483–497. MR 1249616
[11] T. L. Miller and V. G. Miller: An operator satisfying Dunford’s condition $\mathrm (C)$ but without Bishop’s property $(\text{b})$. Glasgow Math. J. 40 (1998), 427–430. DOI 10.1017/S0017089500032754 | MR 1660054
[12] M. M. Neumann: On local spectral properties of operators on Banach spaces. Rend. Circ. Mat. Palermo (2), Suppl. 56 (1998), 15–25. MR 1710819 | Zbl 0929.47001
[13] S. L. Sun: The sum and product of decomposable operators. Northeast. Math. J. 5 (1989), 105–117. (Chinese) MR 1010749 | Zbl 0699.47022
[14] F.-H. Vasilescu: Analytic Functional Calculus and Spectral Decompositions. Editura Academiei and D. Reidel Publ. Company, Bucharest and Dordrecht, 1982. MR 0690957 | Zbl 0495.47013
[15] P. Vrbová: On local spectral properties of operators in Banach spaces. Czechoslovak Math. J. 23(98) (1973), 483–492. MR 0322536
Search
Partner of
