• Khinchin's Inequality, Dunford-Pettis and Compact Operators on the Space $C([0, 1], X)$

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/117/01/0013-0030

• # Keywords

Banach spaces of continuous functions; tensor products; operator ideals; 𝑝-summing operators.

• # Abstract

We prove that if $X, Y$ are Banach spaces, 𝛺 a compact Hausdorff space and $U:C(\Omega,X)\to Y$ is a bounded linear operator, and if 𝑈 is a Dunford–Pettis operator the range of the representing measure $G(\Sigma)\subseteq D P(X, Y)$ 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 $l_p,(1\leq p &lt; \infty)$ be Dunford–Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.

• # Author Affiliations

1. Department of Mathematics, University of Constanta, 8700 Constanta, Romania

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019