Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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.

 

Absolutely continuous functions on idempotent semigroups in the locally convex setting
HTML articles powered by AMS MathViewer

by A. Katsaras PDF
Trans. Amer. Math. Soc. 206 (1975), 329-337 Request permission

Abstract:

Let $E$ be a locally convex space and let $T$ be a semigroup of semicharacters on an idempotent semigroup. It is shown that there exists an isomorphism between the space of $E$-valued functions on $T$ and the space of all $E$-valued finitely additive measures on a certain algebra of sets. The space of all $E$-valued functions on $T$ which are absolutely continuous with respect to a positive definite function $F$ is identified with the space of all $E$-valued measures which are absolutely continuous with respect to the measure ${m_F}$ corresponding to $F$. Finally a representation is given for the operators on the set of all $E$-valued finitely additive measures on an algebra of sets which are absolutely continuous with respect to a positive measure.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E40
  • Retrieve articles in all journals with MSC: 46E40
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 329-337
  • MSC: Primary 46E40
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0374904-2
  • MathSciNet review: 0374904