2-Summing operators on C([0, 1], lp) with values in l1 |
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Authors: | Dumitru Popa |
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Institution: | (1) Department of Mathematics, University of Constanta, Bd. Mamaia 124, 8700 Constanta, Romania |
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Abstract: | Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U
#, U
# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π
s
(C(Ω, X), Y); (β)U
# ∈ Π
s
(C(Ω), Π
s
(X, Y)); (γ) U
# ε Π
s
(X, Π
s
(C(Ω), Y)). A general result, 10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C(0, 1], l
p
) with values in l
1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result. |
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Keywords: | Banach spaces of continuous functions tensor products operator ideals p-summing operators |
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