Abstract
In this paper, we give new results on demicompact linear operators, study some properties and some results on Fredholm and upper semi-Fredholm relations involving demicompact operators. Our results are used to provide a fine description of the essential pseudospectra.
References
[1] W. Y. Akashi, On the perturbation theory for Fredholm operators, Osaka J. Math. 21 (1984), no. 3, 603–612. Suche in Google Scholar
[2] A. Ammar and A. Jeribi, A characterization of the essential pseudospectra on a Banach space, Arab. J. Math. (Springer) 2 (2013), no. 2, 139–145. 10.1007/s40065-012-0065-7Suche in Google Scholar
[3] A. Ammar and A. Jeribi, Measures of noncompactness and essential pseudospectra on Banach space, Math. Methods Appl. Sci. 37 (2014), no. 3, 447–452. 10.1002/mma.2808Suche in Google Scholar
[4] Z. Artstein, Continuous dependence of solutions of operator equations. I, Trans. Amer. Math. Soc. 231 (1977), no. 1, 143–166. 10.1090/S0002-9947-1977-0445351-1Suche in Google Scholar
[5] W. Chaker, A. Jeribi and B. Krichen, Demicompact linear operators, essential spectrum and some perturbation results, Math. Nachr. 288 (2015), no. 13, 1476–1486. 10.1002/mana.201200007Suche in Google Scholar
[6] E. B. Davies, Linear Operators and Their Spectra, Cambridge Stud. Adv. Math. 106, Cambridge University, Cambridge, 2007. Suche in Google Scholar
[7] S. Goldberg, Unbounded Linear Operators: Theory and Applications, McGraw-Hill, New York, 1966. Suche in Google Scholar
[8] D. Hinrichsen and A. J. Pritchard, Robust stability of linear evolution operators on Banach spaces, SIAM J. Control Optim. 32 (1994), no. 6, 1503–1541. 10.1137/S0363012992230404Suche in Google Scholar
[9] A. Jeribi, Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, Cham, 2015. 10.1007/978-3-319-17566-9Suche in Google Scholar
[10] A. Jeribi, Denseness, Bases and Frames in Banach Spaces and Applications, De Gruyter, Berlin, 2018. 10.1515/9783110493863Suche in Google Scholar
[11] A. Jeribi, Perturbation Theory for Linear Operators—Denseness and Bases with Applications, Springer, Singapore, 2021. 10.1007/978-981-16-2528-2Suche in Google Scholar
[12] A. Jeribi and N. Moalla, A characterization of some subsets of Schechter’s essential spectrum and application to singular transport equation, J. Math. Anal. Appl. 358 (2009), no. 2, 434–444. 10.1016/j.jmaa.2009.04.053Suche in Google Scholar
[13] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261–322. 10.1007/BF02790238Suche in Google Scholar
[14] B. Krichen, Relative essential spectra involving relative demicompact unbounded linear operators, Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), no. 2, 546–556. 10.1016/S0252-9602(14)60027-8Suche in Google Scholar
[15] H. J. Landau, On Szegő’s eigenvalue distribution theorem and non-Hermitian kernels, J. Anal. Math. 28 (1975), 335–357. 10.1007/BF02786820Suche in Google Scholar
[16] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I, Ergeb. Math. Grenzgeb. (3) 92, Springer Berlin, 1977. 10.1007/978-3-642-66557-8Suche in Google Scholar
[17] Z. Opial, Nonexpansive and Monotone Mappings in Banach Spaces, Lecture Notes CDS-LN-67-1, Brown University, Providence, 1967. Suche in Google Scholar
[18]
A. Pełczyński,
On strictly singular and strictly cosingular operators. I. Strictly singular and strictly cosingular operators in
[19] W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276–284. 10.1016/0022-247X(66)90027-8Suche in Google Scholar
[20] M. Schechter, Principles of Functional Analysis, 2nd ed., Grad. Stud. Math. 36, American Mathematical Society, Providence, 2002. Suche in Google Scholar
[21] L. N. Trefethen, Pseudospectra of matrices, Numerical Analysis 1991 (Dundee 1991), Pitman Res. Notes Math. Ser. 260, Longman Scientific & Technical, Harlow (1992), 234–266. Suche in Google Scholar
[22] J. M. Varah, The computation of bounds for the invariant subspaces of a general matrixoperator, Ph.D. thesis, Stanford University, 1967. Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings
Artikel in diesem Heft
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings