[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200215

SOME FREDHOLM THEORY RESULTS AROUND RELATIVE DEMICOMPACTNESS CONCEPT

Chaker, Wajdi (Department of New Economy University of Sfax Higher Institute of Comercial Studies of Sfax)
Jeribi, Aref (Department of Mathematics University of Sfax Faculty of Sciences of Sfax)
Krichen, Bilel (Department of Mathematics University of Sfax Faculty of Sciences of Sfax)

Publication Information

Communications of the Korean Mathematical Society / v.36, no.2, 2021 , pp. 313-325 More about this Journal

Abstract

In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

Keywords

Fredholm theory; demicompact operator; essential spectrum;

Citations & Related Records

Reference

1	M. Faierman, R. Mennicken, and M. Moller, A boundary eigenvalue problem for a system of partial differential operators occurring in magnetohydrodynamics, Math. Nachr. 173 (1995), 141-167. https://doi.org/10.1002/mana.19951730110 DOI
2	M. Mokhtar-Kharroubi, Time asymptotic behaviour and compactness in transport theory, European J. Mech. B Fluids 11 (1992), no. 1, 39-68.
3	W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276-284. https://doi.org/10.1016/0022-247X(66)90027-8 DOI
4	C. Schmoeger, Common spectral properties of linear operators A and B such that ABA = A² and BAB = B², Publ. Inst. Math. (Beograd) (N.S.) 79(93) (2006), 109-114. https://doi.org/10.2298/PIM0693109S DOI
5	F. Wolf, On the invariance of the essential spectrum under a change of boundary conditions of partial differential boundary operators, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959), 142-147. DOI
6	W. Y. Akashi, On the perturbation theory for Fredholm operators, Osaka J. Math. 21 (1984), no. 3, 603-612. http://projecteuclid.org/euclid.ojm/1200777440
7	W. V. Petryshyn, Remarks on condensing and k-set-contractive mappings, J. Math. Anal. Appl. 39 (1972), 717-741. https://doi.org/10.1016/0022-247X(72)90194-1 DOI
8	B. Krichen, Relative essential spectra involving relative demicompact unbounded linear operators, Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), no. 2, 546-556. https://doi.org/10.1016/S0252-9602(14)60027-8 DOI
9	A. Jeribi, Spectral theory and applications of linear operators and block operator matrices, Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-17566-9
10	W. Chaker, A. Jeribi, and B. Krichen, Demicompact linear operators, essential spectrum and some perturbation results, Math. Nachr. 288 (2015), no. 13, 1476-1486. https://doi.org/10.1002/mana.201200007 DOI
11	B. A. Barnes, Common operator properties of the linear operators RS and SR, Proc. Amer. Math. Soc. 126 (1998), no. 4, 1055-1061. https://doi.org/10.1090/S0002-9939-98-04218-X DOI
12	N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958.
13	D. E. Edmunds and W. D. Evans, Spectral theory and differential operators, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1987.
14	B. Krichen and D. O'Regan, On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), no. 2, 625-630. DOI
15	I. Gohberg, S. Goldberg, and M. A. Kaashoek, Classes of linear operators. Vol. I, Operator Theory: Advances and Applications, 49, Birkhauser Verlag, Basel, 1990. https://doi.org/10.1007/978-3-0348-7509-7
16	A. Jeribi, N. Moalla, and S. Yengui, S-essential spectra and application to an example of transport operators, Math. Methods Appl. Sci. 37 (2014), no. 16, 2341-2353. https://doi.org/10.1002/mma.1564 DOI
17	T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966.
18	C. Kuratowski, Sur les espaces complets, Fundamenta Mathematicae 1 (1930), no. 15, 301-309. DOI