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1994 | 111 | 2 | 123-152
Tytuł artykułu

Complemented ideals of group algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The existence of a projection onto an ideal I of a commutative group algebra $L^{1}(G)$ depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously asked questions concerning such hulls and some conjectures are presented concerning the classification of these complemented ideals.
Słowa kluczowe
Czasopismo
Rocznik
Tom
111
Numer
2
Strony
123-152
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-04-05
poprawiono
1993-10-25
Twórcy
  • Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 København Ø, Denmark , kepert@danmat.ku.dk
  • Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613, U.S.A.
Bibliografia
  • [1] D. E. Alspach, A characterization of the complemented translation-invariant subspaces of $L^1(ℝ^2)$, J. London Math. Soc. (2) 31 (1985), 115-124.
  • [2] D. E. Alspach, Complemented translation-invariant subspaces, in: Lecture Notes in Math. 1332, Springer, 1988, 112-125.
  • [3] D. E. Alspach and A. Matheson, Projections onto translation-invariant subspaces of $L^1(ℝ)$, Trans. Amer. Math. Soc. (2) 277 (1983), 815-823.
  • [4] D. E. Alspach, A. Matheson and J. M. Rosenblatt, Projections onto translation-invariant subspaces of $L^1(G)$, J. Funct. Anal. 59 (1984), 254-292; Erratum, ibid. 69 (1986), 141.
  • [5] D. E. Alspach, A. Matheson and J. M. Rosenblatt, Separating sets by Fourier-Stieltjes transforms, ibid. 84 (1989), 297-311.
  • [6] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973.
  • [7] J. E. Gilbert, On projections of $L^∞(G)$ onto translation-invariant subspaces, Proc. London Math. Soc. (3) 19 (1969), 69-88.
  • [8] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin, 1963.
  • [9] D. Hilbert and S. Cohn-Vossen, Anschauliche Geometrie, Springer, Berlin, 1932.
  • [10] A. G. Kepert, The range of group algebra homomorphisms, ANU Mathematics Research Reports 022-91, SMS-089-91 (1991).
  • [11] T.-S. Liu, A. van Rooij and J.-K. Wang, Projections and approximate identities for ideals in group algebras, Trans. Amer. Math. Soc. 175 (1973), 469-482.
  • [12] H. P. Rosenthal, Projections onto translation-invariant subspaces of $L^p(G)$, Mem. Amer. Math. Soc. 63 (1966).
  • [13] H. P. Rosenthal, On the existence of approximate identities in ideals of group algebras, Ark. Mat. 7 (1967), 185-191.
  • [14] W. Rudin, Fourier Analysis on Groups, Interscience, New York, 1962.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv111i2p123bwm
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