Property (ω) and the Single-valued Extension Property
Tóm tắt
By the new spectrum originated from the single-valued extension property, we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property (ω) holds. Meanwhile, the relationship between hypercyclic property (or supercyclic property) and property (ω) is discussed.
Tài liệu tham khảo
Aiena, P.: Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic Publishers, Dordrecht, 2004
Aiena, P., Peňa, P.: Variations on Weyl’s theorem. J. Math. Anal. Appl., 324(1), 566–579 (2006)
Amouch, M.: Weyl type theorems for operators satisfying the single-valued extension property. J. Math. Anal. Appl., 326(2), 1476–1484 (2007)
Cao, X. H.: Weyl type theorem and hypercyclic operators. J. Math. Anal. Appl., 323(1), 267–274 (2006)
Cao, X. H., Liu, A. F.: Generalized Kato type operators and property (ω) under perturbations. Linear Algebra Appl., 436(7), 2231–2239 (2012)
Colojoara, I., Foias, C.: Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968
Djordjević, D. S., Dragan, S.: Operators obeying a-Weyl’s theorem. Publ. Math. Debrecen, 55, 283–298 (1999)
Dunford, N.: Spectral theory II, Resolutions of the identity. Pacific J. Math., 2, 559–614 (1952)
Dunford, N.: Spectral operators. Pacific J. Math., 4, 321–354 (1954)
Dunford, N., Schwartz, J. T.: Linear Operators, Wiley, New York, Part I (1958), Part II (1963), Part III, 1971
Harte, R. E.: Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, 1988
Harte, R. E., Lee, W. Y.: Another note on Weyl’s theorem. Trans. Amer. Math. Soc., 349(5), 2115–2124 (1997)
Herrero, D. A.: Limits of hypercyclic and supercyclic operators. J. Funct. Anal., 99(1), 179–190 (1991)
Hilden, H. M., Wallen, L. J.: Some cyclic and non-cyclic and non-cyclic vectors for certain operators. Indiana Univ. Math. J., 23(7), 557–566 (1974)
Kitai, C.: Invariant closed sets for linear operators, Ph.D. Thesis, Univ. of Toronto, Toronto, 1982
Laursen, K. B., Neumann, M. M.: An Introduction to Local Spectral Theory, Clarendon Press, Oxford, 2000
Oudghiri, M.: Weyl’s and Browder’s theorems for operators satisfying the SVEP. Studia Math., 163(1), 85–101 (2004)
Oudghiri, M.: a-Weyl’s theorem and the single valued extension property. Studia Math., 173(2), 193–201 (2006)
Rakočević, V.: On a class of operators. Mat. Vesnik., 37, 423–426 (1985)
Vasilescu, F. H.: Analytic Functional Calculus and Spectral Decompositions, Editura Academiei and D. Reidel Publishing Company, Bucharest and Dordrecht, 1982
Weyl, H.: Über beschränkte quadratische Formen, deren Dikerenz vollstetig ist. Rend. Circ. Mat. Palermo, 27, 373–392 (1909)