Transfer principles for UPFP are shown from X to ℓ₁(X), c₀(X), ℓ∞(X) under cotype or self-similarity hypotheses, implying primariness of the sums and yielding new proofs for primariness of ℓ∞(L_p), c₀(L_1) and UPFP for C[0,1]*.
Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove that the spaces $\ell_p(C(\alpha))$ and $\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $\alpha$ is an ordinal and $1<p\leq\infty$. For the case $p=1$, we establish a general criterion ensuring that $\ell_1(X)$ inherits the uniform primary factorisation property from $X$. As a consequence, $\ell_p(C(K))$ is primary for every compact metrizable space $K$ and every $1 \leq p \leq \infty$.
fields
math.FA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
No indecomposable Banach space has the primary factorisation property; for complex spaces with PFP the quotient B(E)/M_E is purely infinite precisely when non-scalar.
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Preservation of primariness under $\ell_1$-, $c_0$-, and $\ell_\infty$-sums of Banach spaces
Transfer principles for UPFP are shown from X to ℓ₁(X), c₀(X), ℓ∞(X) under cotype or self-similarity hypotheses, implying primariness of the sums and yielding new proofs for primariness of ℓ∞(L_p), c₀(L_1) and UPFP for C[0,1]*.
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Pure infiniteness and primary factorisation
No indecomposable Banach space has the primary factorisation property; for complex spaces with PFP the quotient B(E)/M_E is purely infinite precisely when non-scalar.