Projective limits in harmonic analysis
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- 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
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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