Fredholm formulae and the Riesz theory

A. F. Ruston

Compositio Mathematica (1967)

  • Volume: 18, Issue: 1-2, page 25-48
  • ISSN: 0010-437X

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Ruston, A. F.. "Fredholm formulae and the Riesz theory." Compositio Mathematica 18.1-2 (1967): 25-48. <http://eudml.org/doc/88938>.

@article{Ruston1967,
author = {Ruston, A. F.},
journal = {Compositio Mathematica},
keywords = {functional analysis},
language = {eng},
number = {1-2},
pages = {25-48},
publisher = {P. Noordhoff N. V., Groningen},
title = {Fredholm formulae and the Riesz theory},
url = {http://eudml.org/doc/88938},
volume = {18},
year = {1967},
}

TY - JOUR
AU - Ruston, A. F.
TI - Fredholm formulae and the Riesz theory
JO - Compositio Mathematica
PY - 1967
PB - P. Noordhoff N. V., Groningen
VL - 18
IS - 1-2
SP - 25
EP - 48
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/88938
ER -

References

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  1. S. Banach [1] Théorie des Opérations Linéaires (Warsaw, 1932). Zbl0005.20901JFM58.0420.01
  2. G. Birkhoff and S. Maclane [2] A Survey of Modern Algebra (New York, 1953). Zbl0052.25402MR54551
  3. A.M. Deprit [3] Endomorphismes de Riesz, Ann. Soc. Sci. Bruxelles, Sér. I, 70 (1956), 165— 184. Zbl0074.09303
  4. [4] Sous-espaces vectoriels d'un espace localement convexe séparé, Acad. Roy. Belg. Bull. Cl. Sci. (5), 42 (1956), 1012—1017. Zbl0073.32802
  5. [5] Quelques classes d'homomorphismes dans des espaces vectoriels, Ann. Soc. Sci. Bruxelles, Sér. I, 71 (1956), 5—43. Zbl0102.10202
  6. [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. Zbl0077.31602
  7. [7] Une propriété des homomorphismes d'espaces de Fréchet, Acad. Roy. Belg. Bull. Cl. Sci. (5), 43 (1957), 834—837. Zbl0079.32202
  8. [8] Quelques classes d'endomorphismes d'espaces localement convexes séparés, Ann. Soc. Sci. Bruxelles, Sér. I, 71 (1957), 89—101. Zbl0100.31701
  9. [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. Zbl0088.08903
  10. [10] Un type d'homomorphismes d'espaces localement convexes séparés, Ann. Soc. Sci. Bruxelles, Sér. I, 72 (1958), 5—13. Zbl0084.09803
  11. N. Dunford [11] Spectral theory. I. Convergence to projections, Trans. American Math. Soc., 54 (1943), 185—217. Zbl0063.01185
  12. [12] Spectral theory, Bull. American Math. Soc., 49 (1943), 637—651. Zbl0063.01184
  13. N. Dunford and J.T. Schwartz [13] Linear Operators. I. General Theory (New York and London, 1958). Zbl0084.10402MR117523
  14. I. Fredholm [14] Sur une classe d'équations fonctionnelles, Acta Math., 27 (1903), 365—390. Zbl34.0422.02JFM34.0422.02
  15. L.M. Graves [15] A generalization of the Riesz theory of completely continuous transformations, Trans. American Math. Soc., 79 (1955), 141-149. Zbl0064.37102MR72438
  16. A. Grothendieck [16] Produits tensoriels topologiques et espaces nucléaires, Mem. American Math. Soc. No. 16 (1955). Zbl0123.30301MR75539
  17. [17] La théorie de Fredholm, Bull. Soc. Math. France, 84 (1956), 319—384. Zbl0073.10101
  18. P.R. Halmos [18] Finite Dimensional Vector Spaces (Princeton, 1942). Zbl0063.01886MR6591
  19. H.L. Hamburger and M.E. Grimshaw [19] Linear Transformations in n-dimensional vector space (Cambridge, 1951). Zbl0043.32504MR41355
  20. G.H. Hardy and E.M. Wright [20] An Introduction to the Theory of Numbers (Oxford, 1945). Zbl0020.29201MR67125
  21. E. Hille [21] Functional Analysis and Semi-groups (New York, 1948). Zbl0033.06501MR25077
  22. R. Kultze [22] Zur Theorie Fredholmschen Endomorphismen in nuklearen topologischen Vektorräumen, J. Reine Angew. Math., 200 (1958), 112-124. Zbl0085.32401MR106415
  23. 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. Zbl0037.35702
  24. T. Leżański [24] The Fredholm theory of linear equations in Banach spaces, Studia Math., 13 (1953), 244—276. Zbl0052.12603
  25. [25] Sur les fonctionnelles multiplicatives, Studia Math., 14 (1953), 13—23. Zbl0052.34604
  26. D.E. Littlewood [26] A University Algebra (London, 1958). Zbl0041.35319
  27. C.C. Macduffee [27] The Theory of Matrices (Berlin, 1933). JFM59.0109.02
  28. L. Mirsky [28] An Introduction to Linear Algebra (Oxford, 1955). Zbl0066.26305MR74364
  29. A.D. Michal and R.S. Martin [29] Some expansions in vector space, Journal de Math. (9), 13 (1934), 69-91. Zbl0009.02301JFM60.0327.02
  30. S. Nikolskij [30] Lineare Gleichungen im metrischen Raume, C. R. Acad. Sci. URSS(N.S.), 2 (1936), 315—319. Zbl0015.02502JFM62.0452.03
  31. F. Riesz [31] Über lineare Funktionalgleichungen, Acta Math., 41 (1916), 71—98. JFM46.0635.01
  32. F. Riesz et B. Sz.-Nagy [32] Leçons d'Analyse Fonctionnelle (Budapest, 1952). Zbl0046.33103
  33. 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. Zbl0054.04906MR42612
  34. [34] Direct products of Banach spaces and linear functional equations, Proc. London Math. Soc. (3), 1 (1951), 327—384. Zbl0043.11003
  35. [35] Formulae of Fredholm type for compact linear operators on a general Banach space, Proc. London Math. Soc. (3), 3 (1953), 368—377. Zbl0050.34203
  36. [36] Operators with a Fredholm theory, Journal London Math. Soc., 29 (1954), 318—326. Zbl0055.10902
  37. [37] Fredholm formulae and the Riesz theory, Proc. Int. Cong. Math.1954Amsterdam, 2 (1954), 164-165. 
  38. [38] A note on clorms, Journal London Math. Soc., 32 (1957), 110—112. Zbl0077.10203
  39. R. Schatten [39] A Theory of Cross-spaces (Princeton, 1950). Zbl0041.43502MR36935
  40. R. Sikorski [40] On multiplication of determinants in Banach spaces, Bull. Acad. Polon. Sci. Cl. III, 1 (1953), 219-221. Zbl0052.34702MR60734
  41. [41] On Leżański's determinants of linear equations in Banach spaces, Studia Math., 14 (1953), 24-48. Zbl0052.34701MR61765
  42. [42] On determinants of Leżański and Ruston, Studia Math., 16 (1957), 99-112. Zbl0080.32701MR97725
  43. [43] Determinant systems, Studia Math., 18 (1959), 161-186. Zbl0092.12101MR109289
  44. [44] On Leżański endomorphisms, Studia Math., 18 (1959), 187—189. Zbl0092.12301
  45. [45] The determinant theory in Banach spaces, Colloquium Math., 8 (1961), 141—198. Zbl0103.33202
  46. [46] Remarks on Leżański's determinants, Studia Math., 20 (1961), 145-161. Zbl0103.33301MR126162
  47. F. Smithies [47] The Fredholm theory of integral equations, Duke Math. Journal, 8 (1941), 107—130. Zbl0025.06003JFM67.0376.02
  48. [48] Integral Equations (Cambridge, 1958). 
  49. Angus E. Taylor [49] Introduction to Functional Analysis (New York, 1958). Zbl0081.10202MR98966
  50. E.C. Titchmarsh [50] The Theory of Functions (Oxford, 1939). JFM65.0302.01
  51. J.H. Williamson [51] Compact linear operators in linear topological spaces, Journal London Math. Soc., 29 (1954), 149-156. Zbl0055.10901MR61270
  52. B. Yood [52] Properties of linear transformations preserved under addition of a completely continuous transformation, Duke Math. Journal, 18 (1951), 599—612. Zbl0043.11901
  53. K. Yosida [53] Quasi-completely-continuous linear functional operations, Jap. Journal of Maths., 15 (1939), 297—301. Zbl0022.35804JFM65.0518.02
  54. A.C. Zaanen [54] On linear functional equations, Nieuw Arch. Wiskunde (2), 22 (1948), 269-282. Zbl0030.03402MR24070
  55. [55] Integral transformations and their resolvents in Orlicz and Lebesgue spaces, Compositio Math., 10 (1952), 56-94. Zbl0046.33901MR53395
  56. [56] Linear Analysis (Amsterdam, 1953). 

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