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2000 | 141 | 1 | 53-68
Tytuł artykułu

Non-regularity for Banach function algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A be a unital Banach function algebra with character space $Φ_{A}$. For $x ∈ Φ_{A}$, let $M_{x}$ and $J_{x}$ be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of $J_{x}$ is connected, and that if x does not belong to the Shilov boundary of A then the set ${y ∈ Φ_{A}: M_{x} ⊇ J_{y}}$ has an infinite connected subset. Various related results are given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
141
Numer
1
Strony
53-68
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-27
Twórcy
  • School of Mathematical Sciences, University of Nottingham, NG7 2RD, U.K.
  • Department of Mathematical Sciences, University of Aberdeen, AB24 3UE, U.K.
Bibliografia
  • [1] R. J. Archbold and C. J. K. Batty, On factorial states of operator algebras, III, J. Operator Theory 15 (1986), 53-81.
  • [2] H. G. Dales and A. M. Davie, Quasianalytic Banach function algebras, J. Funct. Anal. 13 (1973), 28-50.
  • [3] J. Dixmier, C*-algebras, North-Holland, Amsterdam, 1982.
  • [4] J. F. Feinstein and D. W. B. Somerset, Strong regularity for uniform algebras, in: Proc. 3rd Function Spaces Conference (Edwardsville, IL, 1998), Contemp. Math. 232, Amer. Math. Soc., 1999, 139-149.
  • [5] P. Gorkin and R. Mortini, Synthesis sets in $H^∞ + C$, Indiana Univ. Math. J., to appear.
  • [6] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, NJ, 1962.
  • [7] J. L. Kelley, General Topology, Van Nostrand, Princeton, NJ, 1955.
  • [8] M. M. Neumann, Commutative Banach algebras and decomposable operators, Monatsh. Math. 113 (1992), 227-243.
  • [9] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. 1, Cambridge Univ. Press, New York, 1994.
  • [10] W. Rudin, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8 (1957), 39-42.
  • [11] W. Rudin, Real and Complex Analysis, Tata McGraw-Hill, New Delhi, 1974.
  • [12] S. Sidney, More on high-order non-local uniform algebras, Illinois J. Math. 18 (1974), 177-192.
  • [13] D. W. B. Somerset, Minimal primal ideals in Banach algebras, Math. Proc. Cambridge Philos. Soc. 115 (1994), 39-52.
  • [14] D. W. B. Somerset, Ideal spaces of Banach algebras, Proc. London Math. Soc. (3) 78 (1999), 369-400.
  • [15] G. Stolzenberg, The maximal ideal space of functions locally in an algebra, Proc. Amer. Math. Soc. 14 (1963), 342-345.
  • [16] E. L. Stout, The Theory of Uniform Algebras, Bogden and Quigley, New York, 1971.
  • [17] J. Wermer, Banach algebras and analytic functions, Adv. Math. 1 (1961), 51-102.
  • [18] D. R. Wilken, Approximate normality and function algebras on the interval and the circle, in: Function Algebras (New Orleans, 1965), Scott-Foresman, Chicago, IL, 1966, 98-111.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv141i1p53bwm
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