Projection constants for 𝐶(𝑆) spaces with the separable projection property

Baker, John Warren

doi:10.1090/S0002-9939-1973-0320707-8

Projection constants for $C(S)$ spaces with the separable projection property
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Proc. Amer. Math. Soc. 41 (1973), 201-204 Request permission

Abstract:

It is shown that if $n$ and $k$ are positive integers and $C({\omega ^n}k)$ is the Banach space of continuous functions on the compact set $\Gamma ({\omega ^n}k) = \{ \alpha |\alpha$ is an ordinal, $\alpha \leqq {\omega ^n}k\}$ then $C({\omega ^n}k) \in P’$ if and only if $\gamma \leqq 2n + 1$. This establishes the value of the projection constant for all $C(S)$ spaces possessing the separable projection property.

References

D. Amir, Continuous functions’ spaces with the separable projection property, Bull. Res. Council Israel Sect. F 10F (1962), 163–164 (1962). MR 150570
D. Amir, Projections onto continuous function spaces, Proc. Amer. Math. Soc. 15 (1964), 396–402. MR 165350, DOI 10.1090/S0002-9939-1964-0165350-3
Richard Arens, Projections on continuous function spaces, Duke Math. J. 32 (1965), 469–478. MR 181882
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

Uncomplemented $C(X)$-subalgebras of $C(X)$

David W. Dean, Projections in certain continuous function spaces $C(H)$ and subspaces of $C(H)$ isomorphic with $C(H)$, Canadian J. Math. 14 (1962), 385–401. MR 144191, DOI 10.4153/CJM-1962-031-2
W. Holsztyński, Continuous mappings induced by isometries of spaces of continuous function, Studia Math. 26 (1966), 133–136. MR 193491, DOI 10.4064/sm-26-2-133-136
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
R. D. McWilliams, On projections of separable subspaces of $(m)$ onto $(c)$, Proc. Amer. Math. Soc. 10 (1959), 872–876. MR 109296, DOI 10.1090/S0002-9939-1959-0109296-3
A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. (Rozprawy Mat.) 58 (1968), 92. MR 227751
A. Pełczyński, On $C(S)$-subspaces of separable Banach spaces, Studia Math. 31 (1968), 513–522. MR 234261, DOI 10.4064/sm-31-5-513-522
Andrew Sobczyk, Projection of the space $(m)$ on its subspace $(c_0)$, Bull. Amer. Math. Soc. 47 (1941), 938–947. MR 5777, DOI 10.1090/S0002-9904-1941-07593-2