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Algebra direct sum decomposition of $ C\sb R(X)$

Authors: R. D. Mehta and M. H. Vasavada
Journal: Proc. Amer. Math. Soc. 98 (1986), 71-74
MSC: Primary 46J10; Secondary 46E25
MathSciNet review: 848878
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Abstract: Let $ A$ and $ B$ be closed subalgebras of $ {C_R}(X)$ with $ 1 \in A$ and $ 1 \notin B$. We give necessary and sufficient conditions for $ A \oplus B = {C_R}(X)$.

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

  • [1] W. G. Bade, The Banach space $ C(S)$, Lecture Notes, vol. 26, Aarhus Univ., Aarhus, 1971.
  • [2] S. D. Fisher, The decomposition of $ {C_r}(K)$ into the direct sum of subalgebras, J. Funct. Anal. 31 (1979), 218-223. MR 525952 (80b:46060)
  • [3] D. E. Marshall and A. G. O'Farrell, Uniform approximation by real functions, Fund. Math. 104 (1979), 203-211. MR 559174 (82j:41035)
  • [4] Z. Semadeni, Banach spaces of continuous functions, Vol. 1, Monografie Mat., Warszawa, 1971.

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Keywords: Direct sum, chain, set of constancy
Article copyright: © Copyright 1986 American Mathematical Society

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