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Języki publikacji
Abstrakty
We consider continuous operators S +T in Banach spaces, where S is Fredholm and T is quasinuclear. By referring to the basic result of the Fredholm theory, i.e. to the expression of the resolvent ( I + λT ) −1 of the operator T as a quotient of entire functions of λ , we derive analogous formulas for generalized inverses of operators S +T. We apply the Plemelj-Smithies formulas describing terms of determinant systems for the quasinuclear perturbations of Fredholm operators.
Rocznik
Tom
Strony
13--26
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn Olsztyn, Poland
Bibliografia
- [1] Fredholm I., Sur une classe d'equations fonctionnelles, Acta Math. 1903, 27, 365-390.
- [2] Grothendieck A., La theorie de Fredholm, Bull. Soc. Math. Fr. 1956, 84, 319-384.
- [3] Ruston A.F., On the Fredholm theory of integral equations for operators belonging to the trace class of a general Banach space, Proc. Lond. Math. Soc. III. Ser. 1951(2), 53, 109- -124.
- [4] Leżański T., The Fredholm theory of linear equations in Banach spaces, Stud. Math. 1953, 13, 244-276.
- [5] Sikorski R., On Leżański's determinants of linear equations in Banach spaces, Stud. Math. 1953, 14, 24-48.
- [6] Sikorski R., Determinant systems, Stud. Math. 1959, 18, 161-186.
- [7] Sikorski R., The determinant theory in Banach spaces, Colloq. Math. 1961, 8, 141-198.
- [8] Buraczewski A., The determinant theory of generalized Fredholm operators, Studia Math. 1963, 22, 265-307.
- [9] Buraczewski A., Sikorski R., Analytic formulae for determinant systems in Banach spaces, Studia Math. 1980, 67, 85-101.
- [10] Pietsch A., Zur Fredholmschen Theorie in lokalkonvexen ɺaR ɺumen, Stud. Math. 1963, 22, 161-179.
- [11] Pietsch A., Eigenvalues and s-Numbers, Cambridge Studies in Advanced Math., Vol. 13, Cambridge Univ. Press, Cambridge 1987.
- [12] König H., A Fredholm determinant theory for p-summing maps in Banach spaces, Math. Ann. 1980, 247, 255-274.
- [13] Gohberg I., Goldberg S., Krupnik N., Traces and determinants of linear operators, Integr. Equat. Oper. Th. 1996, 26, 136-187.
- [14] Gohberg I., Goldberg S., Krupnik N., Hilbert-Carleman and regularized determinants for linear operators, Integr. Equat. Oper. Th. 1997, 27, 10-47.
- [15] Gohberg I., Goldberg S., Krupnik N., Generalization of the determinants for trace-potent linear operators, Integr. Equat. Oper. Th. 2001, 40, 441-453.
- [16] Plemelj J., Zur Theorie der Fredholmschen Funktionalgleichung, Monat. Math. Phys. 1904, 15, 93-128.
- [17] Carleman T., Zur Theorie der linearen Integralgleichungen, Math. Zeit. 1921, 9, 196-217.
- [18] Smithies F., The Fredholm theory of integral equations, Duke Math. J. 1941, 107-130.
- [19] Smithies F., Integral Equations, Cambridge Univ. Press, Cambridge 1970.
- [20] Ciecierska G., On some application of algebraic quasinuclei to the determinant theory, Journal of Applied Mathematics and Computational Mechanics 2013, 12(3), 27-38.
- [21] Ciecierska G., Determinant systems for nuclear perturbations of Fredholm operators in Frechet spaces, International Publications USA, Panam. Math. J. 2014, 24(1), 1-20.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b9caa6ec-dc8c-4881-b5e5-1d3b54f421f1