Khinchin's Inequality, Dunford-Pettis and Compact Operators on the Space ð??¶([0, 1], ð?‘‹)

Proceedings Mathematical Sciences

Dumitru Popa¹ 

[1] Department of Mathematics, University of Constanta, 00 Constanta, Romania$$

关键词: Banach spaces of continuous functions;    tensor products;    operator ideals;    ð?‘?-summing operators.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We prove that if 𝑋, 𝑌 are Banach spaces, 𝛺 a compact Hausdorff space and 𝑈:𝐶(𝛺,𝑋) → 𝑌 is a bounded linear operator, and if 𝑈 is a Dunford–Pettis operator the range of the representing measure $G(𝛴)subseteq D P(X, Y)$ is an uniformly Dunford–Pettis family of operators and $|G|$ is continuous at $emptyset$. 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 $c_0$ or $l_p,(1≤ p < ∞)$ be Dunford–Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.

【 授权许可】

Unknown