Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Representation of set valued operators
HTML articles powered by AMS MathViewer

by Nikolaos S. Papageorgiou PDF
Trans. Amer. Math. Soc. 292 (1985), 557-572 Request permission


In this paper we prove representation theorems for set valued additive operators acting on the spaces $L_X^1(X = {\text {separable Banach space)}}$, ${L^1}$ and ${L^\infty }$. Those results generalize well-known ones for single valued operators and among them the celebrated Dunford-Pettis theorem. The properties of these representing integrals are studied. We also have a differentiability result for multifunctions analogous to the one that says that an absolutely continuous function from a closed interval into a Banach space with the Radon-Nikodým property is almost everywhere differentiable and also it is the primitive of its strong derivative. Finally we have a necessary and sufficient condition for the set of integrable selectors of a multifunction to be $w$-compact in $L_X^1$. This result is a new very general result about $w$-compactness in the Lebesgue-Bochner space $L_X^1$.
Similar Articles
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 557-572
  • MSC: Primary 47H99; Secondary 28B20, 46E30, 46G99
  • DOI:
  • MathSciNet review: 808737