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Integral representation of multilinear continuous operators from the space of Lebesgue-Bochner summable functions into any Banach space


Author: Witold M. Bogdanowicz
Journal: Bull. Amer. Math. Soc. 72 (1966), 317-320
DOI: https://doi.org/10.1090/S0002-9904-1966-11511-2
MathSciNet review: 0187117
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  • 1. S. Banach, Ueber homogene polynome in L2, Studia Math. 7 (1938), 36-44.
  • 2. W. M. Bogdanowicz, A generalization of the Lebesgue-Bochner-Stieltjes integral and a new approach to the theory of integration, Proc. Nat. Acad. Sci. U. S. A. 53 (1965), 492-498. MR 176030
  • 3. W. M. Bogdanowicz, Integral representations of linear continuous operators from the space of Lebesgue-Bochner summable functions into any Banach space, Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 351-354. MR 187084
  • 4. W. M. Bogdanowicz, Integral representations of linear continuous operators on L, Bull. Acad. Polon. Sci. (1965).
  • 5. W. M. Bogdanowicz, An approach to the theory of L, Bull. Acad. Polon. Sci. (1965).
  • 6. W. M. Bogdanowicz, An approach to the theory of Lebesgue-Bochner measurable functions and to the theory of measure, Math. Ann. (to appear). MR 201601
  • 7. W. M. Bogdanowicz, An approach to the theory of intration generated by positive functionals and integral representations of linear continuous functionals on the space of vector-valued continuous functions, Math. Ann. (to appear).
  • 8. W. M. Bogdanowicz, Multilinear Lebesgue-Bochner-Stieltjes integral Bull. Amer. Math. Soc. 72 (1966), 232-236. MR 190284
  • 9. W. M. Bogdanowicz, Fubini theorems for generalized Lebesgue-Bochner-Stieltjes integral, Trans. Amer. Math. Soc. (to appear). MR 201602
  • 10. N. Bourbaki, Integration, Actualités Sci. Ind., Chapters I-IV, No. 1175 (1952); Chapter V, No. 1244 (1956); Chapter VI, No. 1281 (1959).
  • 11. J. Dieudonné, Sur le théorème de Lebesgue-Nikodym. Y, Canad. J. Math. 3 (1951), 129-139. MR 44611
  • 12. N. Dinculeanu, Sur la représentation intégrale des certaines opérations linéaires. II, Compositio Math. 14 (1959), 1-22. MR 104148
  • 13. N. Dinculeanu, Sur la représentation intégrale des certaines opérations linéaires. III, Proc. Amer. Math. Soc. 10 (1959), 59-68. MR 104149
  • 14. N. Dunford and B. J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323-392. MR 2020
  • 15. N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York, 1958.
  • 16. G. Fichtenholz and L. Kantorovitch, Sur les opérations linéares dans l'espace des fonction bornées, Studia Math. 5 (1934), 69-98.
  • 17. C. Foias and I. Singer, Some remarks on the representation of linear operators in spaces of vector-valued continuous functions. Rev. Math. Pures Appl. 5 (1960), 729-752. MR 131770
  • 18. E. Hille and R. S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ. Vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 89373
  • 19. A. Grothendieck, Sur les applications linéaires faiblement compàctes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. MR 58866
  • 20. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955), 1-191. MR 75539
  • 21. P. R. Halmos, Measure theory, Van Nostrand, New York, 1950. MR 33869
  • 22. T. H. Hildebrandt, On bounded linear functional operations, Trans. Amer. Math. Soc. 36 (1934), 865-875. MR 1501772
  • 23. R. S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108-136. MR 7938
  • 24. F. Riesz, Sur les opérations fonctionelles linéaires, C.R. Acad. Sci. Paris 149 (1909), 974-977.
  • 25. F. Riesz and Sz. B. Nagy, Leçons d'analyse fonctionelle, Akadémiai Kiadó, Budapest, 1952.
  • 26. I. Singer, Sur les applications linéaires intégrales des espaces des fonctions continues à valeurs vectorielles, Acta Math. Acad. Sci. Hungar. 11 (1960), 3-13. MR 115081
  • 27. M. H. Stone, Notes on integration, Proc. Nat. Acad. Sci. U.S.A., (a) I 34 (1948), 336-342; (b) II 34 (1948), 447-455; (c) III 34 (1948), 483-490; (d) IV 35 (1949), 50-58.
  • 28. K. Swong, A representation theory of continuous linear maps, Math. Ann. 155 (1964), 270-291. MR 165358


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DOI: https://doi.org/10.1090/S0002-9904-1966-11511-2

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