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- Title
2-Summing operators on C([0, 1], l<sub>p</sub>) with values in l<sub>1</sub>.
- Authors
Popa, Dumitru
- Abstract
Let ω be a compact Hausdorff space, X a Banach space, C(ω,X) the Banach space of continuousX-valued functions on ω under the uniform norm,U: C(ω,X) → Y a bounded linear operator andU#,U# two natural operators associated to U. For each 1 ⩽ s < ∞, let the conditions (α) U ϵ πs(C(ω,X), Y ); (β)U# ϵ πs(C(ω),πs(X, Y )); (γ) U# ϵ πs(X,πs(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], lp) with values in l1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result.
- Subjects
HAUSDORFF measures; BANACH spaces; LINEAR operators; ABSOLUTELY summing operators; MATHEMATICS
- Publication
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2009, Vol 119, Issue 2, p221
- ISSN
0253-4142
- Publication type
Article
- DOI
10.1007/s12044-009-0022-3