S Spectral Theory of Multivalued Linear Operator in Banach Spaces
Download PDF
Authors: A. AMMAR, A. JERIBI AND B. SAADAOUI
DOI: 10.46793/KgJMat2608.1313A
Abstract:
In this paper, we begin with the definition of the S-resolvent set of a linear relation. Throughout this paper, X will denote a normed linear space over the complex field ℂ. Operator S plays the role of a transition multivalued linear operator from X. It is the main goal of the present note to study the basic spectral properties of T linked to the transition multivalued linear operator S.
Keywords:
S-resolvent, S-spectra, linear relation, Banach space.
References:
[1] T. Alvarez, A. Ammar and A. Jeribi, On the essential spectra of some matrix of lineair relations, Math. Methods Appl. Sci. 37 (2014), 620–644.
[2] T. Alvarez, A. Ammar and A. Jeribi, A characterization of some subsets of S-essential spectra of a multivalued linear operator, Col. Math. 135(2) (2014), 171–186.
[3] A. Ammar, A. Jeribi and B. Saadaoui, Frobenius-Schur factorization for multivalued 2×2 matrices linear operator, Mediterr. J. Math. 14(1) (2017), 14–29.
[4] A. Ammar, A. Jeribi and B. Saadaoui, A characterization of essential pseudospectra of the multivalued operator matrix, Anal. Math. Phys. 8(3) (2018), 325–350. https://link.springer.com/article/10.1007/s13324-017-0170-z
[5] A. Ammar, A. Jeribi and B. Saadaoui, On some classes of demicompact linear relation and some results of essential pseudospectra, Mat. Stud. 52 (2019), 195–210. http://matstud.org.ua
[6] A. Ammar, A. Jeribi and B. Saadaoui, Demicompactness, selection of linear relation and application to multivalued matrix, Filomat 36(7) (2022), 2215–2235. https://doiserbia.nb.rs/img/doi/0354-5180/2022/0354-51802207215A.pdf
[7] A. Ben Ali and B. Saadaoui, On the condition spectrum of linear operator pencils, Palermo (2) 72(3) (2023), 1845–1861. https://link.springer.com/article/10.1007/s12215-022-00756-5
[8] A. G. Baskakov and K. I. Chernyshov, Spectral analysis of linear relations and degenerate operator semigroups, Sb. Math. 193 (2003), 1573–1610. https://iopscience.iop.org/article/10.1070/SM2002v193n11ABEH000696/pdf
[9] T. Berger and C. Trunk and H. Winkler, Linear relations and the Kronecker canonical form, Linear Algebra Appl. 488 (2016), 13–44. https://math.uni-paderborn.de
[10] R. W. Cross, Multivalued Linear Operators, Marcel Dekker, 1998. https://bibliotekanauki.pl
[11] A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1999. https://eudml.org/doc/164036
[12] I. C. Gohberg and M. G. Krein, The basic propositions on defect numbers, root numbers and indices of linear operators, Amer. Math. Soc. Transl. (2) 13 (1960), 185–264. https://app.dimensions.ai/details/publication/pub.1089183012
[13] A. Jeribi, Spectral Theory and Applications of Linear operator and Block Operator Matrices, Springer-Verlag, New York, 2015. https://link.springer.com/book/10.1007/978-3-319-17566-9
[14] M. Kostić, Abstract Degenerate Volterra Integro-Differential Equations, Mathematical Institute SANU, Belgrade, 2020. http://www.mi.sanu.ac.rs/publications
[15] B. Saadaoui, On (P,Q)-outer generalized inverses and their stability of pseudo spectrum, Southeast Asian Bull. Math. 46(5) (2022), 633–647. http://www.seams-bull-math.ynu.edu.cn
[16] B. Saadaoui, Characterization of the condition S-spectrum of a compact operator in a right quaternionic Hilbert space, Rend. Circ. Mat. Palermo (2) 72(1) (2023), 707–724. http://springer.com/article/10.1007/s12215-021-00700-z?fromPaywallRec=true
[17] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, Second Edition, John Wiley Sons, New York-Chichester-Brisbane, 1980.
Login:
