Traces and determinants of linear operators

Israel Gohberg1, Seymour Goldberg2, Naum Krupnik3
1School of Mathematics Sachler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel
2Department of Mathematics, University of Maryland, College Park, USA
3Dept. of Math. and Comp. Science, Bar-Ilan University, Ramat-Gan, Israel

Tóm tắt

Từ khóa


Tài liệu tham khảo

[BA]. Ben-Artzi, A.,Traces of compact operators, Integr. Equat. Oper. Th., 7 (1984), 310?324.

[Bo]. Bobr, St.,Eine Verallgemeinerung des von Koch'schen Satzen über die absolute Konvergenz der uneedlichen Determinanten, Math. Z. 10 (1921), 1?11.

[Ca]. Carleman, T.,Zur Theorie der Linearen Integralgleichungen Math. Zeit., 9 (1921), 196?217.

[C1]. Cohen, L. W.,A note on system of equations with infinite many unknowns, Bull. A. M. S.36 (2), (1930), 563?572.

[C2]. Cohen, L. W.,Transformations on spaces of infinitely many dimensions, Annals of Math.37 (2), (1936), 326?335.

[DS]. Dunford, N., Schwartz, J.,Linear Operators, Vol. II. Spectral Theory, Interscience, 1963.

[FS]. Fenyö, S., Stolle, H.,Theorie und Praxis der Linearen Integralgleichungen, Vol. I?IV, Birkhäuser, 1982?1984.

[Fr]. Fredholm, I.,Sur une Classe d'Equation Fonctionelles, Acta Math. 27 (1903), 365?390.

[GGK]. Gohberg, I., Goldberg, S., Kaashoek, M. A.,Classes of Linear Operators, Vol. I, Birkhäuser Verlag, Basel, 1990.

[GKa]. Gohberg, I., Kaashoek, M. A.,Asymptotic formulas of Szegö-Kac-Achiezer type, Asymptotic Analysis 5 (1992), North-Holland, 187?220

[GK]. Gohberg, I., Krein, M.,Introduction to the Theory of Linear Non-Self Adjoint Operators, Translations AMS, 18, 1969.

[Gr]. Grothendieck, A.,La Theory de Fredholm, Bull. Soc. Math. France84, (1956), 319?384.

[Gu]. Goursat, M.,Sur une cas élémentaire de l'équation de Fredholm, Bulletin de la Société mathématique, vol.XXXV, fask.III, (1907), 163?173.

[Hi]. Hilbert, D.,Grundzuge einer allgemeinen Theorie det linearen Integralgleichungen I., Nach. Wiss. Math. Phys. Gott. (1904), 49?91

[It]. Itskovich, I.,On Fredholm series, Doklady AN SSSR, Vol LIX, N3, (1948), 423?426.

[K1]. Von Koch, H.,Sur la Convergence des Déterminants Infinis Rend. Circ. Mat. Palermo28 (1909), 255?266.

[K2]. Von Koch, H.,Sur les Déterminants Infinis et les Équations Differentielles Linéares, Acta Math.16, (1892), 271?295.

[Le]. Lezanski, T.,The Fredholm Theory of Linear Equations in Banach Spaces, Studia Math., 13 (1953), 244?276.

[Mi]. Mikhlin, S.,On the convergence of Fredholm series, Doklady AN SSSR, Vol.XLII, N9, (1944), 374?377.

[MW]. Mennicken, R., Wagenführer, E.,Über die Konvergenz verallgemeinerter Hillscher Determinanten. Math. Nachr.72 (1976), 21?49.

[Pi]. Pietsch, A.,Eigenvalues and s-numbers, Cambridge Studies in Advanced Math. Vol.13, Cambridge Univ. Press, Cambridge, 1987.

[Pl]. Plemelj, J.,Zur Theorie Fredholmshen Functionalgleichung, Monat. für Math. und Phys., 15 (1907), 93?128.

[Po]. Poincaré, H.,Sur les déterminants d'ordre infini Bull. Soc. Math. France14 (1886), 77?90.

[Ri]. Riesz, F.,Les Syst?mes D'equations Linéaires a une infinité d'inconnues, Collection de monographies sur la théorie des functions, Paris, 1913.

[Ru]. Ruston, A. F., Fredholm theory in Banach spaces, Cambridge University Press, Cambridge, 1986.

[Si]. Sikorski, R.,The Determinant Theory in Banach sppaces, Colloq. Math.8, (1961), 141?198.

[Si1]. Simon, B.,Trase ideals and their applications, Lecture Note Series 35, London, 1979.

[Si2]. Simon, B.,Notes on Infinite Determinants of Hilbert Space Operators, Adv. Math. 24 (1977), 244?273.

[SS]. Seiler, E., Simon, B.,An Inequality for Determinants, Proc. Nat. Acad. Sci., 72 (1975), 3277?3278.

[Sm]. Smithies, F.,Integral Equations, Cambridge University Press, 1965.