On a theorem of a Pełczyński

Gamlen, John L. B.

doi:10.1090/S0002-9939-1974-0341036-3

On a theorem of a Pełczyński
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by John L. B. Gamlen

Proc. Amer. Math. Soc. 44 (1974), 283-285

DOI: https://doi.org/10.1090/S0002-9939-1974-0341036-3

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Abstract:

If $Y$ is a weakly complete Banach space, and $X$ is a Banach space with separable dual, then every continuous linear operator from ${C_X}(K)$ to $Y$ must be weakly compact. Here ${C_X}(K)$ denotes the space of continuous functions on the compact Hausdorff space $K$, having values in $X$.

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