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.

 

Projective limits in harmonic analysis
HTML articles powered by AMS MathViewer

by William A. Greene PDF
Trans. Amer. Math. Soc. 209 (1975), 119-142 Request permission

Abstract:

A treatment of induced transformations of measures and measurable functions is presented. Given a diagram $\varphi :G \to H$ in the category of locally compact groups and continuous proper surjective group homomorphisms, functors are produced which on objects are given by $G \to {L^2}(G),{L^1}(G)$, $M(G),W(G)$, denoting, resp., the ${L^2}$-space, ${L^1}$-algebra, measure algebra, and von Neu mann algebra generated by left regular representation of ${L^1}$ on ${L^2}$. All functors but but the second are shown to preserve projective limits; by example, the second is shown not to do so. The category of Hilbert spaces and linear transformations of norm $\leqslant 1$ is shown to have projective limits; some propositions on such limits are given. Also given is a type and factor characterization of projective limits in the category of ${W^ \ast }$-algebras and surjective normal $\ast$-algebra homomorphisms.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 22D15, 43A95
  • Retrieve articles in all journals with MSC: 22D15, 43A95
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 119-142
  • MSC: Primary 22D15; Secondary 43A95
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0376952-5
  • MathSciNet review: 0376952