Fredholm formulae and the Riesz theory
Ruston, A. F.
Compositio Mathematica, Tome 18 (1967), p. 25-48 / Harvested from Numdam
Publié le : 1967-01-01
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     author = {Ruston, A. F.},
     title = {Fredholm formulae and the Riesz theory},
     journal = {Compositio Mathematica},
     volume = {18},
     year = {1967},
     pages = {25-48},
     mrnumber = {221331},
     zbl = {0184.16102},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1967__18_1-2_25_0}
}
Ruston, A. F. Fredholm formulae and the Riesz theory. Compositio Mathematica, Tome 18 (1967) pp. 25-48. http://gdmltest.u-ga.fr/item/CM_1967__18_1-2_25_0/

S. Banach [1] Théorie des Opérations Linéaires (Warsaw, 1932). | JFM 58.0420.01 | Zbl 0005.20901

G. Birkhoff and S. Maclane [2] A Survey of Modern Algebra (New York, 1953). | MR 54551 | Zbl 0052.25402

A.M. Deprit [3] Endomorphismes de Riesz, Ann. Soc. Sci. Bruxelles, Sér. I, 70 (1956), 165- 184. | Zbl 0074.09303

[4] Sous-espaces vectoriels d'un espace localement convexe séparé, Acad. Roy. Belg. Bull. Cl. Sci. (5), 42 (1956), 1012-1017. | Zbl 0073.32802

[5] Quelques classes d'homomorphismes dans des espaces vectoriels, Ann. Soc. Sci. Bruxelles, Sér. I, 71 (1956), 5-43. | Zbl 0102.10202

[6] Une partition du spectre d'un endomorphisme continu d'un espace vectoriel topologique complexe, Nederl. Akad. Wetensch. Proc. Ser. A, 60 (1957), 55-59. | Zbl 0077.31602

[7] Une propriété des homomorphismes d'espaces de Fréchet, Acad. Roy. Belg. Bull. Cl. Sci. (5), 43 (1957), 834-837. | Zbl 0079.32202

[8] Quelques classes d'endomorphismes d'espaces localement convexes séparés, Ann. Soc. Sci. Bruxelles, Sér. I, 71 (1957), 89-101. | Zbl 0100.31701

[9] Contribution à l'étude de l'algèbre des applications linéaires continues d'un espace localement convexe séparé: Théorie de Riesz - théorie spectrale, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8° 31 (1959), no. 2. | Zbl 0088.08903

[10] Un type d'homomorphismes d'espaces localement convexes séparés, Ann. Soc. Sci. Bruxelles, Sér. I, 72 (1958), 5-13. | Zbl 0084.09803

N. Dunford [11] Spectral theory. I. Convergence to projections, Trans. American Math. Soc., 54 (1943), 185-217. | Zbl 0063.01185

[12] Spectral theory, Bull. American Math. Soc., 49 (1943), 637-651. | Zbl 0063.01184

N. Dunford and J.T. Schwartz [13] Linear Operators. I. General Theory (New York and London, 1958). | MR 117523 | Zbl 0084.10402

I. Fredholm [14] Sur une classe d'équations fonctionnelles, Acta Math., 27 (1903), 365-390. | JFM 34.0422.02

L.M. Graves [15] A generalization of the Riesz theory of completely continuous transformations, Trans. American Math. Soc., 79 (1955), 141-149. | MR 72438 | Zbl 0064.37102

A. Grothendieck [16] Produits tensoriels topologiques et espaces nucléaires, Mem. American Math. Soc. No. 16 (1955). | MR 75539 | Zbl 0123.30301

[17] La théorie de Fredholm, Bull. Soc. Math. France, 84 (1956), 319-384. | Numdam | Zbl 0073.10101

P.R. Halmos [18] Finite Dimensional Vector Spaces (Princeton, 1942). | MR 6591 | Zbl 0063.01886

H.L. Hamburger and M.E. Grimshaw [19] Linear Transformations in n-dimensional vector space (Cambridge, 1951). | MR 41355 | Zbl 0043.32504

G.H. Hardy and E.M. Wright [20] An Introduction to the Theory of Numbers (Oxford, 1945). | MR 67125 | Zbl 0020.29201

E. Hille [21] Functional Analysis and Semi-groups (New York, 1948). | MR 25077 | Zbl 0033.06501

R. Kultze [22] Zur Theorie Fredholmschen Endomorphismen in nuklearen topologischen Vektorräumen, J. Reine Angew. Math., 200 (1958), 112-124. | MR 106415 | Zbl 0085.32401

J. Leray [23] Valeurs propres et vecteurs propres d'un endomorphisme complètement continu d'un espace vectoriel à voisinages convexes, Acta Sci. Math. Szeged, 12 Pars B (1950), 177-186. | Zbl 0037.35702

T. Leżański [24] The Fredholm theory of linear equations in Banach spaces, Studia Math., 13 (1953), 244-276. | Zbl 0052.12603

[25] Sur les fonctionnelles multiplicatives, Studia Math., 14 (1953), 13-23. | Zbl 0052.34604

D.E. Littlewood [26] A University Algebra (London, 1958). | Zbl 0041.35319

C.C. Macduffee [27] The Theory of Matrices (Berlin, 1933). | JFM 59.0109.02

L. Mirsky [28] An Introduction to Linear Algebra (Oxford, 1955). | MR 74364 | Zbl 0066.26305

A.D. Michal and R.S. Martin [29] Some expansions in vector space, Journal de Math. (9), 13 (1934), 69-91. | JFM 60.0327.02 | Zbl 0009.02301

S. Nikolskij [30] Lineare Gleichungen im metrischen Raume, C. R. Acad. Sci. URSS(N.S.), 2 (1936), 315-319. | JFM 62.0452.03 | Zbl 0015.02502

F. Riesz [31] Über lineare Funktionalgleichungen, Acta Math., 41 (1916), 71-98. | JFM 46.0635.01

F. Riesz et B. Sz.-Nagy [32] Leçons d'Analyse Fonctionnelle (Budapest, 1952). | Zbl 0046.33103

A.F. Ruston [33] On the Fredholm theory of integral equations for operators belonging to the trace class of a general Banach space, Proc. London Math. Soc. (2), 53 (1951), 109-124. | MR 42612 | Zbl 0054.04906

[34] Direct products of Banach spaces and linear functional equations, Proc. London Math. Soc. (3), 1 (1951), 327-384. | Zbl 0043.11003

[35] Formulae of Fredholm type for compact linear operators on a general Banach space, Proc. London Math. Soc. (3), 3 (1953), 368-377. | Zbl 0050.34203

[36] Operators with a Fredholm theory, Journal London Math. Soc., 29 (1954), 318-326. | Zbl 0055.10902

[37] Fredholm formulae and the Riesz theory, Proc. Int. Cong. Math. 1954 Amsterdam, 2 (1954), 164-165.

[38] A note on clorms, Journal London Math. Soc., 32 (1957), 110-112. | Zbl 0077.10203

R. Schatten [39] A Theory of Cross-spaces (Princeton, 1950). | MR 36935 | Zbl 0041.43502

R. Sikorski [40] On multiplication of determinants in Banach spaces, Bull. Acad. Polon. Sci. Cl. III, 1 (1953), 219-221. | MR 60734 | Zbl 0052.34702

[41] On Leżański's determinants of linear equations in Banach spaces, Studia Math., 14 (1953), 24-48. | MR 61765 | Zbl 0052.34701

[42] On determinants of Leżański and Ruston, Studia Math., 16 (1957), 99-112. | MR 97725 | Zbl 0080.32701

[43] Determinant systems, Studia Math., 18 (1959), 161-186. | MR 109289 | Zbl 0092.12101

[44] On Leżański endomorphisms, Studia Math., 18 (1959), 187-189. | Zbl 0092.12301

[45] The determinant theory in Banach spaces, Colloquium Math., 8 (1961), 141-198. | Zbl 0103.33202

[46] Remarks on Leżański's determinants, Studia Math., 20 (1961), 145-161. | MR 126162 | Zbl 0103.33301

F. Smithies [47] The Fredholm theory of integral equations, Duke Math. Journal, 8 (1941), 107-130. | JFM 67.0376.02 | Zbl 0025.06003

[48] Integral Equations (Cambridge, 1958).

Angus E. Taylor [49] Introduction to Functional Analysis (New York, 1958). | MR 98966 | Zbl 0081.10202

E.C. Titchmarsh [50] The Theory of Functions (Oxford, 1939). | JFM 65.0302.01

J.H. Williamson [51] Compact linear operators in linear topological spaces, Journal London Math. Soc., 29 (1954), 149-156. | MR 61270 | Zbl 0055.10901

B. Yood [52] Properties of linear transformations preserved under addition of a completely continuous transformation, Duke Math. Journal, 18 (1951), 599-612. | Zbl 0043.11901

K. Yosida [53] Quasi-completely-continuous linear functional operations, Jap. Journal of Maths., 15 (1939), 297-301. | JFM 65.0518.02 | Zbl 0022.35804

A.C. Zaanen [54] On linear functional equations, Nieuw Arch. Wiskunde (2), 22 (1948), 269-282. | MR 24070 | Zbl 0030.03402

[55] Integral transformations and their resolvents in Orlicz and Lebesgue spaces, Compositio Math., 10 (1952), 56-94. | Numdam | MR 53395 | Zbl 0046.33901

[56] Linear Analysis (Amsterdam, 1953).