Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Banach bundles of continuous functions and an integral representation theorem


Author: Anthony Karel Seda
Journal: Trans. Amer. Math. Soc. 270 (1982), 327-332
MSC: Primary 28C05; Secondary 22A30, 46H99, 46M99
DOI: https://doi.org/10.1090/S0002-9947-1982-0642344-8
MathSciNet review: 642344
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A construction is given of a Banach bundle $p:A \to X$ whose fibres are spaces of continuous functions which vanish at infinity. A Riesz type integral representation theorem is established which describes all functional on $A$.


References [Enhancements On Off] (What's this?)

  • Sterling K. Berberian, Measure and integration, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1965. MR 0183839
  • N. Bourbaki, IntĂ©gration. III: ElĂ©ments de mathĂ©matique, Hermann, Paris, 1959.
  • Charles W. Burden, The Hahn-Banach theorem in a category of sheaves, J. Pure Appl. Algebra 17 (1980), no. 1, 25–34. MR 560783, DOI https://doi.org/10.1016/0022-4049%2880%2990021-3
  • J. M. G. Fell, An extension of Mackey’s method to Banach $^{\ast } $ algebraic bundles, Memoirs of the American Mathematical Society, No. 90, American Mathematical Society, Providence, R.I., 1969. MR 0259619
  • ---, Induced representations and Banach $^{\ast }$-algebraic bundles, Lecture Notes in Math., vol. 582, Springer-Verlag, Berlin and New York, 1977.
  • Jean Renault, A groupoid approach to $C^{\ast } $-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. MR 584266
  • A. K. Seda, Haar measures for groupoids, Proc. Roy. Irish Acad. Sect. A 76 (1976), no. 5, 25–36. MR 427598
  • Anthony Karel Seda, Quelques rĂ©sultats dans la catĂ©gorie des groupoĂŻdes d’opĂ©rateurs, C. R. Acad. Sci. Paris SĂ©r. A-B 288 (1979), no. 1, A21–A24 (French, with English summary). MR 522010
  • Joel J. Westman, Harmonic analysis on groupoids, Pacific J. Math. 27 (1968), 621–632. MR 244443

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28C05, 22A30, 46H99, 46M99

Retrieve articles in all journals with MSC: 28C05, 22A30, 46H99, 46M99


Additional Information

Article copyright: © Copyright 1982 American Mathematical Society