## Rocky Mountain Journal of Mathematics

### New criteria for the weak Radon-Nikodým property related to set-valued operators

Keun Young Lee

#### Abstract

In this paper, we deal with new equivalent conditions for the localized weak Radon-Nikod\'ym property in dual Banach space related to set-valued operators. First, we introduce the geometric definition of the weak Radon-Nikod\'ym property and the weakly fragmented set-valued operator. Next, using the weakly fragmented mapping, we reveal the relation between the weak Radon-Nikod\'ym property and the weakly single-valued operator. Finally, using this relation and the concept of the exposed point, the main theorem is given together with some applications.

#### Article information

Source
Rocky Mountain J. Math., Volume 45, Number 5 (2015), 1511-1526.

Dates
First available in Project Euclid: 26 January 2016

https://projecteuclid.org/euclid.rmjm/1453817252

Digital Object Identifier
doi:10.1216/RMJ-2015-45-5-1511

Mathematical Reviews number (MathSciNet)
MR3452226

Zentralblatt MATH identifier
1352.46018

#### Citation

Lee, Keun Young. New criteria for the weak Radon-Nikodým property related to set-valued operators. Rocky Mountain J. Math. 45 (2015), no. 5, 1511--1526. doi:10.1216/RMJ-2015-45-5-1511. https://projecteuclid.org/euclid.rmjm/1453817252

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