[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2015.28.3.419

THE LOCALIZED SINGLE-VALUED EXTENSION PROPERTY AND LOCAL SPECTRAL THEORY

YOO, JONG-KWANG (Department of Liberal Arts and Science Chodang University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.28, no.3, 2015 , pp. 419-429 More about this Journal

Abstract

In this paper, we study properties SVEP, Bishop's property ( ${\beta}$ ), property ( ${\delta}$ ), decomposability, property $({\beta})_{\epsilon}$ , subscalarity, Kato spectrum, generalized Kato decomposition, finite ascent for bounded linear operators in Banach spaces.

Keywords

single-valued extension property; Bishop's property ( ${\beta}$ ); generalized Kato decomposition; Kato spectrum;

Citations & Related Records

Reference

1	P. Aiena, Fredholm and local spectral theory, with application to multipliers, Kluwer Acad., 2004.
2	P. Aiena and O. Monsalve, Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), no. 2, 435-448. DOI ScienceOn
3	P. Aiena and M. Gonzalez, On the Dunford property (C) for bounded linear operators RS and SR, Integral Equations Operator Theory 70 (2011), 561-568. DOI
4	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: Advances and Applications, Birkhauser Verlag, Basel 17 (1986), 15-34.
5	C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1984), 279-294.
6	B. A. Barnes, Common operator properties of the linear operators RS and SR, Proc. Amer. Math. Soc. 126 (1998), no. 4, 1055-1061. DOI ScienceOn
7	C. Benhida and E. H. Zerouali, Local spectral theory of linear operators RS and SR, Integral Equations Operator Theory 54 (2006), 1-8. DOI
8	I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
9	N. Dunford, Spectral theory II. Resolution of the identity, Pacific J. Math. 2 (1952), 559-614. DOI
10	N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. DOI
11	N. Dunford and J. T. Schwartz, Linear operators, Part III: Spectral operators, Wiley, New York, 1971.
12	J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61-69. DOI
13	H. Heuser, Functional Analysis, Marcel Dekker, New York, 1982.
14	K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press, Oxford Science Publications, Oxford, 2000.
15	T. L. Miller, V. G. Miller, and M. M. Neumann, Spectral subspaces of subscalar and related operators, Proc. Amer. Math. Soc. 132 (2004), 1483-1493. DOI ScienceOn
16	C. Lin, Z. Yan, and Y. Ruan, p-Hyponormal operators are subscalar, Proc. Amer. Math. Soc. 131 (2003), 2753-2759. DOI ScienceOn
17	M. Mbekhta, Resolvant generalise et theorie spectrale, J. Operator Theory 21 (1989), 69-105.
18	M. Mbekhta and A. Ouahab, Operateur s-regulier dans un espace de Banach et theorie spectrale, Acta Sci. Math. (Szeged) 59 (1994), 525-543.
19	C. Schmoeger, Common spectral properties of linear operators A and B such that ABA = $A^2$ and BAB = $B^2$ , Publ. de L'Inst. math. (NS) 79(93) (2006), 109-114. DOI
20	C. Schmoeger, On the operators equations ABA = $A^2$ and BAB = $B^2$ , Publ. de L'Inst. Math(NS) 78(92) (2006), 127-133. DOI
21	A. Taylor and D. Lay, Introduction to functional analysis, 2nd Edition, Wiley, New York, 1980.
22	J.-K Yoo, Subscalar operators with property ( ${\delta}$ ) have invariant subspace, Bull. KMS. 48 (2011), no. 6, 1129-1135.