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An Abstract Dauns-Hofmann-Kaplansky Multiplier Theorem

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
Mathematics Institute, University of Copenhagen
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The present investigation was stimulated by a theorem of Alfsen and Effros (4.9 of [1]) concerning a real Banach space, its ikf-ideals, and its primitive M-ideals (these are denned in [1]). This theorem states that a real Banach space is in the natural way a module over the ring of bounded continuous real-valued functions on the space of primitive Jlf-ideals with the Jacobson topology.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 827 - 836
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Alfsen, E. M. and Effros, E. G., Structure in real Banach spaces, Part II, Ann. of Math. 96 (1972), 129–173.Google Scholar
2. Dauns, J. and Hofmann, K. H., Representations of rings by continuous sections, Mem. Amer. Math. Soc. 83 (1968).Google Scholar
3. Elliott, G. A. and Olesen, D., A simple proof of the Dauns-Hofmann theorem, Math. Scand. 34 (1974), 231–234.Google Scholar
4. Kaplansky, I., The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255.Google Scholar