Algebra direct sum decomposition of 𝐶_{𝑅}(𝑋). II

Mehta, R. D.; Vasavada, M. H.

doi:10.1090/S0002-9939-1987-0883413-7

Algebra direct sum decomposition of $C_ R(X)$. II
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by R. D. Mehta and M. H. Vasavada PDF

Proc. Amer. Math. Soc. 100 (1987), 123-126 Request permission

Abstract:

We give conditions under which the sets of constancy of a closed subalgebra of ${C_R}(X)$, which is complemented by a closed subalgebra, are retracts of $X$.

References

The Banach space

John Warren Baker, Some uncomplemented subspaces of $C(X)$ of the type $C(Y)$, Studia Math. 36 (1970), 85–103. MR 275356, DOI 10.4064/sm-36-2-85-103
Stephen D. Fisher, The decomposition of $C_{r}(K)$ into the direct sum of subalgebras, J. Functional Analysis 31 (1979), no. 2, 218–223. MR 525952, DOI 10.1016/0022-1236(79)90062-4
Donald E. Marshall and Anthony G. O’Farrell, Uniform approximation by real functions, Fund. Math. 104 (1979), no. 3, 203–211. MR 559174, DOI 10.4064/fm-104-3-203-211
R. D. Mehta and M. H. Vasavada, On the direct sum decomposition of an algebra of continuous functions, Bull. Austral. Math. Soc. 32 (1985), no. 1, 69–71. MR 811289, DOI 10.1017/S0004972700009722
R. D. Mehta and M. H. Vasavada, Algebra direct sum decomposition of $C_R(X)$, Proc. Amer. Math. Soc. 98 (1986), no. 1, 71–74. MR 848878, DOI 10.1090/S0002-9939-1986-0848878-4

Banach spaces of continuous functions

Hisa-aki Yoshizawa, On simultaneous extension of continuous functions, Proc. Imp. Acad. Tokyo 20 (1944), 653–654. MR 15776