Complemented copies of 𝑐₀ in vector valued Hardy spaces

Dowling, Patrick N.

doi:10.1090/S0002-9939-1989-0984786-9

Complemented copies of $c_ 0$ in vector valued Hardy spaces
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Proc. Amer. Math. Soc. 107 (1989), 251-254 Request permission

Abstract:

Let $X$ be a complex Banach space containing a copy of ${c_0}$, let $\mathbb {T}$ be the unit circle and let $D$ be the open unit disk in the complex plane. Then ${H^p}(\mathbb {T},X)$ contains a complemented copy of ${c_0}$ for $1 \leq p < \infty$. The corresponding result for ${H^p}(D,X)$ fails for $1 \leq p \leq \infty$.

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On complemented copies of

in injective tensor products

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