Duality Theorems for Kac Algebras and Locally Compact Groups

Michel Enock and Jean-Marie Schwartz
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Michel Enock: Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales
Jean-Marie Schwartz: Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales

Chapter Chapter 4 in Kac Algebras and Duality of Locally Compact Groups, 1992, pp 124-160 from Springer

Abstract: Abstract In that chapter, we obtain a duality theorem for Kac algebras, namely that the bidual Kac algebra is isomorphic to the original Kac algebra (4.1.1). From that, we can successively deduce that the Fourier representation a is faithful, and that M* is semi-simple (4.1.3). We also see that the dual Kac algebra of the Kac algebra 한s(G) constructed in Chap. 3 is the Kac algebra 한a(G) constructed in Chap. 2 (4.1.2). These results were found, independently, by the authors in [36], and Vainermann and Kac in [180].

Keywords: Spectral Measure; Compact Group; Haar Measure; Duality Theorem; Fourier Representation (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-3-662-02813-1_5

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