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)

 
 

 

Finite codimensional ideals in function algebras


Author: Krzysztof Jarosz
Journal: Trans. Amer. Math. Soc. 287 (1985), 779-785
MSC: Primary 46J10
DOI: https://doi.org/10.1090/S0002-9947-1985-0768740-9
MathSciNet review: 768740
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Assume $ S$ is a compact, metric space and let $ M$ be a finite codimensional closed subspace of a complex space $ C(S)$. In this paper we prove that if each element from $ M$ has at least $ k$ zeros in $ S$, then for some $ {s_1}, \ldots ,{s_k} \in S,M \subseteq \{ f \in C(S):f({s_1}) = \cdots = f({s_k}) = 0\} $.


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

  • [1] B. Aupetit, Une généralisation du théorème de Gleason-Kahane-Żelazko pour les algèbres de Banach, Pacific J. Math. 85 (1979), 11-17. MR 571623 (82a:46044)
  • [2] Chang-Pao Chen, A generalization of the Gleason-Kahane-Żelazko theorem, Pacific J. Math. 107 (1983), 81-87. MR 701808 (85d:46070)
  • [3] N. Farnum and R. Whitley, Functionals on real $ C(S)$, Canad. J. Math. 30 (1978), 490-498. MR 0473798 (57:13459)
  • [4] A. M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171-172. MR 0213878 (35:4732)
  • [5] J. P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343. MR 0226408 (37:1998)
  • [6] S, Kowalski and Z. Słodkowski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math. 67 (1980), 215-223. MR 592387 (82d:46070)
  • [7] M. Roitman and Y. Sternfeld, When is a linear functional multiplicative?, Trans. Amer. Math. Soc. 267 (1981), 111-124. MR 621976 (82j:46061)
  • [8] C. R. Warner and R. Whitley, A characterization of regular maximal ideals, Pacific J. Math. 30 (1969), 277-281. MR 0415331 (54:3420)
  • [9] -, Ideals of finite codimension in $ C[0,1]$ and $ {L^1}(R)$, Proc. Amer. Math. Soc. 76 (1979), 263-267. MR 537085 (81b:46070)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46J10

Retrieve articles in all journals with MSC: 46J10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0768740-9
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society