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1995 | 115 | 2 | 189-205
Tytuł artykułu

Topologies on the space of ideals of a Banach algebra

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely $τ_∞$, coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra $τ_∞$ coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if $τ_∞$ is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A) with the relative hull kernel topology turn out to be separable Lindelöf spaces if A is separable, which improves results from [14].
Słowa kluczowe
Czasopismo
Rocznik
Tom
115
Numer
2
Strony
189-205
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-12-28
poprawiono
1995-03-02
Twórcy
  • Mathematisches Institut der Universität Münster, Einsteinstr. 62, 48149 Münster, Fed. Rep. Germany
Bibliografia
  • [1] R. J. Archbold, Topologies for primal ideals, J. London Math. Soc. (2) 36 (1987), 524-542.
  • [2] R. J. Archbold and D. W. B. Somerset, Quasi-standard C*-algebras, Math. Proc. Cambridge Philos. Soc. 107 (1990), 349-360.
  • [3] F. Beckhoff, The minimal primal ideal space of a C*-algebra and local compactness, Canad. Math. Bull. (4) 34 (1991), 440-446.
  • [4] F. Beckhoff, The minimal primal ideal space and AF-algebras, Arch. Math. (Basel) 59 (1992), 276-282.
  • [5] F. Beckhoff, The minimal primal ideal space of a separable C*-algebra, Michigan Math. J. 40 (1993), 477-492.
  • [6] F. Beckhoff, The adjunction of a unit and the minimal primal ideal space, in: Proc. 2nd Internat. Conf. in Funct. Anal. and Approx. Theory, Acquafredda di Maratea, September 14-19, 1992, Rend. Circ. Mat. Palermo (2) Suppl. 33 (1993), 201-209.
  • [7] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
  • [8] H. G. Dales, On norms on algebras, in: Proc. Conf. Canberra 1989, Centre for Mathematical Analysis, Australian National University, Vol. 21, 1989, 61-96.
  • [9] R. S. Doran and V. A. Belfi, Characterizations of C*-algebras, Marcel Dekker, 1986.
  • [10] R. A. Hirschfeld and W. Żelazko, On spectral norm Banach algebras, Bull. Acad. Polon. Sci. 16 (1968), 195-199.
  • [11] W. Rudin, Fourier Analysis on Groups, Interscience, 1962.
  • [12] W. Rudin, Functional Analysis, McGraw-Hill, 1973.
  • [13] S. Sakai, C*-algebras and W*-algebras, Springer, 1971.
  • [14] D. W. B. Somerset, Minimal primal ideals in Banach algebras, Math. Proc. Cambridge Philos. Soc. 115 (1994), 39-52.
  • [15] A. Wilansky, Between $T_1$ and $T_2$, Amer. Math. Monthly 74 (1967), 261-266.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv115i2p189bwm
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