Khinchin's inequality, Dunford--Pettis and compact operators on the space \pmbC([0,1],X)

2007/03/21 by Dumitru Popa, Popa, Dumitru
Computer Science · Mathematics · #46B28 #47A80 #47B10 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B28 #msc:47A80 #msc:47B10

paper · pdf · doi:10.48550/arxiv.math/0703626

18 pages

arxiv created 2007/03/21 · openalex publication_date 2007/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if X,Y are Banach spaces, Ω a compact Hausdorff space and U\hbox\rm : C(Ω,X)→ Y is a bounded linear operator, and if U is a Dunford--Pettis operator the range of the representing measure G(Σ) ⊆ DP(X,Y) is an uniformly Dunford--Pettis family of operators and ‖G‖ is continuous at ∅. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space C([0,1],X) with values in c₀ or l_p, (1≤ p<∞) be Dunford--Pettis and/or compact operators, in which, Khinchin's inequality plays an important role.

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