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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1975, Volume 18, Issue 1, Pages 91–96 (Mi mz7629)

Uncomplemented uniform algebras

S. V. Kislyakov

Abstract: Let $A$ be a closed subalgebra of the algebra of all complex-valued continuous functions on a compact space $X$, and suppose $A$ contains the constant functions and separates points of $X$; let $I$ be a closed ideal of $A$ such that for some linear multiplicative functional $\varphi$ on $A$ we have the relation $0<\|\varphi|_I\|<1$ (for the existence of such an ideal it is sufficient that in the maximal ideal space of the algebra $A$ there exists a Gleason part consisting of at least two points). Then the Banach space $A^{**}$ is not injective [in particular, $A$ is not a complemented subspace of $C(X$)].

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English version:
Mathematical Notes, 1974, 18:1, 637–639

Bibliographic databases:

UDC: 517

Citation: S. V. Kislyakov, “Uncomplemented uniform algebras”, Mat. Zametki, 18:1 (1975), 91–96; Math. Notes, 18:1 (1974), 637–639

Citation in format AMSBIB
\Bibitem{Kis75} \by S.~V.~Kislyakov \paper Uncomplemented uniform algebras \jour Mat. Zametki \yr 1975 \vol 18 \issue 1 \pages 91--96 \mathnet{http://mi.mathnet.ru/mz7629} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=388106} \zmath{https://zbmath.org/?q=an:0312.46062} \transl \jour Math. Notes \yr 1974 \vol 18 \issue 1 \pages 637--639 \crossref{https://doi.org/10.1007/BF01461145}