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Segal algebras and dense ideals in Banach algebras

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Functional Analysis and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 399))

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References

  1. Bochner, S., Uber factorfolgen für Fouriersche reihen, Acta. Sci. Math. (Szeged) 4 (1928) 125–129.

    Google Scholar 

  2. Bourbaki, N., Elements de Mathematique Fasc. 32 theories Spectrales, Hermann, Paris 1967.

    Google Scholar 

  3. Brainerd, B. and Edwards, R.E., Linear operators which commute with translations, I and II. J. Austr. Math. Soc. VI (1966) 289–350.

    Article  MathSciNet  Google Scholar 

  4. Burnham, J.T., Closed ideals in subalgebras of Banach algebras I, Proc. Amer. Math. Soc. 32 (1972) 551–555.

    Article  MathSciNet  MATH  Google Scholar 

  5. Burnham, J.T., Closed ideals in subalgebras of Banach algebras II: Ditkin's condition, to appear in Monatsh. für Math.

    Google Scholar 

  6. Burnham, J.T., Nonfactorization in Subsets of the measure algebra, Proc. Amer. Math. Soc. 35 (1972) 104–106.

    Article  MathSciNet  MATH  Google Scholar 

  7. Burnham, J.T., Topics in the multiplier theory of commutative Segal algebras, to be submitted for publication.

    Google Scholar 

  8. Burnham, J.T. and Goldberg, Richard, R., Basic properties of Segal algebras, to appear in J. for Math. Analysis and Applications.

    Google Scholar 

  9. Butzer, P.L. and Nessel, R.J., Fourier Analysis and Approximation, Vol. I: One-Dimensional theory, Academic Press, New York 1971.

    Book  Google Scholar 

  10. Carleman, T. L'Integral de Fourier et questions qui s'y rattachent, Inst. Mittag-Leffler Publ. Scient., Uppsala 1944 (Lectures given at the Mittag-Leffler Institute in 1935).

    Google Scholar 

  11. Cigler, J., Normed ideas in L1(G), Nederl. Akad. Wetensch. Proc. Ser. A 72=Indag. Math. 31 (1969) 273–282.

    MathSciNet  Google Scholar 

  12. Ditkin, V.A., Study of the structure of ideals in certain normed rings, Ucenye Zapiski Moskov. Gos. Unive. Matematika 30 (1939) 83–130 (in Russian).

    MathSciNet  Google Scholar 

  13. Dunford, N. and Schwartz, J.T., Linear Operators, Part II: Spectral theory, self adjoint operators in Hilbert Space, Interscience Publishers, Inc., New York, 1963.

    MATH  Google Scholar 

  14. Edwards, R.E., Comments on Wiener's Tauberian theorems, J. London Math. Soc. 33 (1958) 462–466.

    Article  MathSciNet  MATH  Google Scholar 

  15. Edwards, R.E., Fourier Series: A Modern Introduction, Vols. I and II, Holt Reinhart and Winston, New York, 1967.

    Google Scholar 

  16. Edwards, R.E., Integration and Harmonic Analysis on Compact Groups, London Mathematical Society Lecture Notes Series 8, Cambridge University Press, 1972.

    Google Scholar 

  17. Gohberg, I.C. and Krein, M.G., Introduction to the theory of linear nonselfadjoint operators, Translations of Math. Monographs Vol.18 Amer. Math. Soc. 1969.

    Google Scholar 

  18. Goldberg, R.R., On a space of functions of Wiener, Duke Math. J. 34 (1967) 683–691.

    Article  MathSciNet  MATH  Google Scholar 

  19. Glicksberg, I., When is μ*L closed, Trans. Amer. Math. Soc.1972.

    Google Scholar 

  20. Hardy, G.H., Divergent Series, Oxford University Press, New York, 1949.

    MATH  Google Scholar 

  21. Hewitt, E. and Ross, K.A., Abstract Harmonic Analysis, Vol.II: Structure and Analysis for Compact Groups and Locally Compact Abelian Groups, Springer-Verlag: Berlin-Gottingen-Heidelberg 1970.

    MATH  Google Scholar 

  22. Iwasawa, K., On group rings of topological rings, Proc. Imp. Acad. Japan, Tokyo 20 (1944) 67–70.

    Article  MathSciNet  Google Scholar 

  23. Johnson, B.E., Some examples in harmonic analysis Preprint 1972.

    Google Scholar 

  24. Katznelson, Y., An Introduction to Harmonic Analysis, John Wiley and Sons, Inc., 1968.

    Google Scholar 

  25. Kitchen, J.W. Jr., Normed modules and almost periodicity, Monatsh. Für Math. 70 (1966) 233–243.

    Article  MathSciNet  MATH  Google Scholar 

  26. Korenblyum, B.I., On certain special commutative normed rings, Doklady Akad. Nauk, SSSR (N.W.) 64 (1949) 281–287 (In Russian).

    MathSciNet  Google Scholar 

  27. Lai, H-C., On some properties of AP(G)-algebras, Proc. Japan Acad. 45 (1969) 572–576.

    Article  MathSciNet  MATH  Google Scholar 

  28. Lai, H-C., On the category of L1(G) ∩ LP(G) in Aq (G), Proc. Japan Acad. 45 (1969) 577–581.

    Article  MathSciNet  MATH  Google Scholar 

  29. Larsen, R., Liu, T-S. and Wang, J-K., On functions with Fourier transforms in Lp, Michigan Math. J. 11 (1964) 369–378.

    Article  MathSciNet  MATH  Google Scholar 

  30. de Leeuw, K., Homogeneous algebras on compact groups, Trans. Amer. Math. Soc. 87 (1958) 372–386.

    MathSciNet  MATH  Google Scholar 

  31. Lipsman, R., Abstract Harmonic Analysis, Yale University, 1968.

    Google Scholar 

  32. Liu, T-S., Sums and intersections of normed linear spaces, Math. Nachr. 42 (1969) 29–42.

    Article  MathSciNet  MATH  Google Scholar 

  33. Loomis, L., Abstract Harmonic Analysis, D. Van Nostrand and Company 1952.

    Google Scholar 

  34. Martin, J.C. and Yap, L.Y.H., The algebra of functions with Fourier transforms in LP, Proc. Amer. Math. Soc. 24 (1970) 217–219.

    MathSciNet  MATH  Google Scholar 

  35. Mirkil, H., The Work of Shilov on Commutative Semi-Simple Banach Algebras, Fasciculo Pelo Instituto de Mathematical Pura e Aplicada, Rio de Janeiro, 1966.

    Google Scholar 

  36. Pitt, H.R., Tauberian Theorems, Oxford University Press 1958.

    Google Scholar 

  37. Reiter, H., Subalgebras of L1(G), Nederl. Akad. Wetensch. Proc. Ser. A 68 (1965) 691–696.

    MathSciNet  MATH  Google Scholar 

  38. Reiter, H., Classical Harmonic Analysis and Locally Compact Groups, Oxford 1968.

    Google Scholar 

  39. Reiter, H., L1-Algebras and Segal Algebras, Lecture Notes in Mathematics, No. 231 Springer-Verlag: Berlin-Heidelberg-New York 1971.

    Google Scholar 

  40. Ross, K.A., Some new characterizations of Sidon sets (for details consult reference 1 therein) in Conference on Harmonic Analysis, Lecture Notes in Mathematics, No.266 Springer-Verlag, Berlin-Heidelberg-New York 1972.

    Google Scholar 

  41. Salem, R., Sur les transformations des séries de Fourier, Fund. Math. 33 (1939).

    Google Scholar 

  42. Segal, I., The group ring of a locally compact group I, Proc. Nat. Acad. Sci., U.S.A. 27 (1940) 348–352.

    Article  Google Scholar 

  43. Segal, I., The group algebra of a locally compact group, Trans. Amer. Math. Soc. 61 (1947) 69–105.

    Article  MathSciNet  MATH  Google Scholar 

  44. Schatten, R., A Theory of Cross Spaces, Ann. of Math. Stud. No.26, Princeton University Press, 1950.

    Google Scholar 

  45. Schatten, R., Norm Ideals of Completely Continuous Operators, Springer-Verlag: Berlin-Gottingen-Heidelberg, 1960.

    Book  MATH  Google Scholar 

  46. Shilov, G.E., Homogeneous rings of functions, Uspehi Mat. Nauk. (N.S.) 41 (1951) 91–137 (In Russian) English translation: Translations of the Amer. Math. Soc. Series 1 Vol.8 (1962) 392–455.

    Google Scholar 

  47. Wang, J-K., Lectures on Banach Algebras, Lecture notes, Department of Mathematics, Yale University, 1965.

    Google Scholar 

  48. Wang, H-C., Non-factorization in Group Algebras, Ph.D. thesis, The University of Iowa, Iowa City, Iowa, 1971. To appear in revised form in Studia Math.

    Google Scholar 

  49. Warner, C.R., Closed ideals in the group algebra L1(G) ∩ L2(G), Trans. Amer. Math. Soc. 121 (1966) 408–423.

    MathSciNet  MATH  Google Scholar 

  50. Widder, D.V., The Laplace Transform, Princeton University Press, Princeton, 1941.

    Google Scholar 

  51. Wiener, N., Tauberian Theorems, MIT Press 1964, 143–242 (Reprinting of Wiener's 1932 Acta. Paper).

    Google Scholar 

  52. Wiener, N., The Fourier Integral and Certain of Its Applications, Cambridge University Press 1933.

    Google Scholar 

  53. Yap, L.Y.H., Ideals in subalgebras of the group algebras, Studia Math. 35 (1970) 165–175.

    MathSciNet  MATH  Google Scholar 

  54. Yap, L.Y.H., Non-factorization in Fréchet subalgebras of L1(G), Preprint 1971.

    Google Scholar 

  55. Williamson, J.H., On theorems of Kawada and Wendel, Proc. Edinburgh Math. Soc. 11 (1958–59).

    Google Scholar 

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Authors
  1. James T. Burnham
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H. G. Garnir K. R. Unni J. H. Williamson

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Burnham, J.T. (1974). Segal algebras and dense ideals in Banach algebras. In: Garnir, H.G., Unni, K.R., Williamson, J.H. (eds) Functional Analysis and its Applications. Lecture Notes in Mathematics, vol 399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063565

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  • DOI: https://doi.org/10.1007/BFb0063565

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  • Print ISBN: 978-3-540-06869-3

  • Online ISBN: 978-3-540-37827-3

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