Rocky Mountain Journal of Mathematics

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

Keun Young Lee

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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

Permanent link to this document
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

Subjects
Primary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10]
Secondary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]

Keywords
Radon-Nikodým weakly fragmented set-valued operator weakly single-valued operator $x^{**}$-weak$^{*}$ exposed point

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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