New results of spectra and pseudospectra of multivalued linear operators. (English) Zbl 07920304
Summary: In this paper, we give some properties and results of stability related to the \(S\)-spectra, \(S\)-pseudospectra, \(S\)-essential spectra and \(S\)-essential pseudospectra of multivalued linear operators and we show some of their characteristics.
MSC:
| 47A55 | Perturbation theory of linear operators |
References:
| [1] | A. Ammar and A. Jeribi, Spectral theory of multivalued linear operators. Apple Academic Press, Oakville, ON; CRC Press, Boca Raton, FL, [2022], 2022. xviii+295 pp. ISBN: 978-1-77188-966-7; 978-1-77463-938-2; 978-1-00313-112-0. · Zbl 1471.47001 |
| [2] | T. Alvarez, A. Ammar and A. Jeribi, A Characterization of some subsets of S-essential spectra of a multivalued linear operator. Colloq. Math. 135, no. 2, 171-186 (2014). · Zbl 1318.47005 |
| [3] | T. Alvarez, A. Ammar and A. Jeribi, On the essential spectra of some matrix of linear relations. Math. Methods Appl. Sci. 37, no. 5, 620-644, (2014). · Zbl 1331.47001 |
| [4] | T. Alvarez, R. W. Cross and D. Wilcox, Multivalued Fredholm type operators with abstract generalised inverses. J. Math. Anal. Appl. 261, no. 1, 403-417, (2001). · Zbl 0993.47012 |
| [5] | T. Alvarez, Linear relations on hereditarily indecomposable normed spaces. Bull. Aust. Math. Soc. 84, no. 1, 49-52, (2011). · Zbl 1221.47006 |
| [6] | T. Alvarez, On almost semi-Fredholm linear relations in normed spaces. Glasg. Math. J. 47 , no. 1, 187-193, (2005). · Zbl 1090.47001 |
| [7] | T. Alvarez, Linear relations on hereditarily indecomposable normed spaces. Bull. Aust. Math. Soc. 84, no. 1, 49-52 (2011). · Zbl 1221.47006 |
| [8] | A. Ammar and A. Jeribi, A characterization of the essential pseudospectra on a Banach space. J. Arab. Math., 2 139-145 (2013). · Zbl 1296.47004 |
| [9] | A. Ammar and A. Jeribi, A characterization of the essential pseudospectra and application to a transport equation. Extracta Math., 28 95-112 (2013). · Zbl 1308.47012 |
| [10] | A. Ammar and A. Jeribi, Measures of noncompactness and essential pseudospectra on Banach space. Math. Meth. Appl. Sci., 37 447-452 (2014). · Zbl 1321.47084 |
| [11] | A. Ammar, H. Daoud, A. Jeribi, Pseudospectra and essential pseudospectra of multivalued linear relations. Mediterr. J. Math. 12 , no. 4, 1377-139 (2015). · Zbl 1357.47006 |
| [12] | A. Ammar, H. Daoud and A. Jeribi, The stability of pseudospectra and essential pseudospectra of linear relations.. J. Pseudo-Differ. Oper. Appl. 7 , no. 4, 473-491 (2016). · Zbl 06768755 |
| [13] | A. Ammar, H. Daoud and A. Jeribi, S-pseudospectra and S-essential pseudospectra. Matematicki Vesnik, 72 no. 2, 95-105 (2020). · Zbl 1474.47006 |
| [14] | R. Arens, Operational calculus of linear relations. Pacific J. Math. 11, 9-23, (1961). · Zbl 0102.10201 |
| [15] | E. A. Coddington, Extension theory of formally normal and symmetric subspaces. Memoirs of the American Mathematical Society, no. 134. American Mathematical Society, Providence, R.I, 1973. · Zbl 0265.47023 |
| [16] | R. W. Cross, Multivalued linear operators. Monographs and Textbooks in Pure and Applied Mathematics, 213. Marcel Dekker, Inc., New York, 1998. · Zbl 0911.47002 |
| [17] | E. B. Davies, Linear operators and their spectra. United States of America by Cambridge University Press, New York, 2007. · Zbl 1138.47001 |
| [18] | A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution equations. Annali di Matematoca Pura ed Applicata ; 353-384 (1993). · Zbl 0786.47037 |
| [19] | D. Hinrichsen and A. J. Pritchard, Robust stability of linear operators on Banach spaces. J. Cont. Opt. 32, 1503-1541 (1994). · Zbl 0817.93055 |
| [20] | A. Jeribi, Spectral theory and applications of linear operators and block operator matrices. Springer-Verlag, New York, 2015. · Zbl 1354.47001 |
| [21] | Jeribi, A: Denseness, bases and frames in Banach spaces and applications. (English) Zbl 06849137 Berlin : De Gruyter (ISBN 978-3-11-048488-5/hbk ; 978-3-11-049386-3/ebook). xv, 406 p. (2018). · Zbl 1437.46003 |
| [22] | Jeribi, A: Perturbation theory for linear operators: Denseness and bases with applications. Springer-Verlag (ISBN 978-981-16-2527-5), Singapore (2021). · Zbl 1483.47001 |
| [23] | H. J. Landau, On Szego’s eigenvalue distribution theorem and non-Hermitian kernels. J. Analyse Math. 28, 335-357 (1975). · Zbl 0321.45005 |
| [24] | J. Von. Neumann, Uber adjungierte Funktional-operator en. Ann. Math. 33, 294-310 (1932). · Zbl 0004.21603 |
| [25] | L. N. Trefethen, Pseudospectra of matrices. Numerical analysis 1991 (Dundee, 1991), Pitman Res. Notes Math. Ser. 260, Longman Sci. Tech., Harlow 234-266 (1992). · Zbl 0798.15005 |
| [26] | J. M. Varah, The computation of bounds for the invariant subspaces of a general matrix operator. Thesis (Ph.D.)-Stanford University. ProQuest LLC, Ann Arbor, MI (1967). |
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