Demicompactness perturbation in Banach algebras and some stability results
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Slim Chelly
Abstract
In this paper, we introduce and investigate a new concept that we call
demicompact elements in Banach algebras as a generalization of demicompact linear
operators acting on Banach spaces. Our concept is used to construct a new class of
Fredholm perturbations with respect to a given Banach subalgebra B, that contains
an inessential ideal
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] B. A. Barnes, Perturbation theory relative to a Banach algebra of operators, Studia Math. 106 (1993), no. 2, 153–174. 10.4064/sm-106-2-153-174Suche in Google Scholar
[3] B. A. Barnes, The spectrum of elements of a commutative LMC-algebra relative to a Banach subalgebra, Rocky Mountain J. Math. 27 (1997), no. 2, 425–445. 10.1216/rmjm/1181071921Suche in Google Scholar
[4] B. A. Barnes, Fredholm theory in an algebra with respect to a Banach subalgebra, Math. Proc. R. Ir. Acad. 101A (2001), no. 1, 7–19. Suche in Google Scholar
[5] B. A. Barnes, G. J. Murphy, M. R. F. Smyth and T. T. West, Riesz and Fredholm Theory in Banach Algebras, Res. Notes Math. 67, Pitman, Boston, 1982. Suche in Google Scholar
[6] A. Ben Ali and N. Moalla, Fredholm perturbation theory and some essential spectra in Banach algebra with respect to subalgebra, Indag. Math. (N. S.) 28 (2017), no. 2, 276–286. 10.1016/j.indag.2016.06.014Suche in Google Scholar
[7] 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
[8] N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Pure Appl. Math. 7, Interscience, New York, 1958. Suche in Google Scholar
[9] I. C. Gohberg and M. G. Kreĭn, The basic propositions on defect numbers, root numbers and indices of linear operators, Amer. Math. Soc. Transl. (2) 13 (1960), 185–264. 10.1090/trans2/013/08Suche in Google Scholar
[10] I. C. Gohberg, A. S. Markus and I. A. Fel’dman, Normally solvable operators and ideals associated with them, Bul. Akad. Štiince RSS Moldoven. 1960 (1960), no. 10(76), 51–70. 10.1090/trans2/061/03Suche in Google Scholar
[11] M. González and A. Martínez-Abejón, Tauberian Operators, Oper. Theory Adv. Appl. 194, Birkhäuser, Basel, 2010. 10.1007/978-3-7643-8998-7Suche in Google Scholar
[12] 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
[13] A. Jeribi, B. Krichen and M. Salhi, Characterization of relatively demicompact operators by means of measures of noncompactness, J. Korean Math. Soc. 55 (2018), no. 4, 877–895. Suche in Google Scholar
[14] K. Jörgens, Linear Integral Operators, Surv. Reference Works Math. 7, Pitman, Boston, 1982. Suche in Google Scholar
[15] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Grundlehren Math. Wiss. 132, Springer, Berlin, 1976. Suche in Google Scholar
[16] K. Latrach and A. Dehici, Fredholm, semi-Fredholm perturbations, and essential spectra, J. Math. Anal. Appl. 259 (2001), no. 1, 277–301. 10.1006/jmaa.2001.7501Suche in Google Scholar
[17] 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
[18] W. V. Petryshyn, Remarks on condensing and k-set-contractive mappings, J. Math. Anal. Appl. 39 (1972), 717–741. 10.1016/0022-247X(72)90194-1Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
Artikel in diesem Heft
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
