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Approximately Periodic Functionals on C*-Algebras and von Neumann Algebras

Published online by Cambridge University Press:  20 November 2018

John C. Quigg
John C. Quigg*
Affiliation:
Arizona State University, Tempe, Arizona
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In the duality for locally compact groups, much use is made of a version of the Hopf algebra technique in the context of von Neumann algebras, culminating in the theory of Kac algebras [6], [14]. It seems natural to ask whether something like a Hopf algebraic structure can be defined on the pre-dual of a Kac algebra. This leads to the question of whether the multiplication on a von Neumann algebra M, viewed as a linear map m from M ⊙ M (the algebraic tensor product) to M, can be pre-transposed to give a co-multiplication on the pre-dual M*, i.e., a linear map m* from M* to the completion of M* ⊙ M* with respect to some cross-norm. A related question is whether the multiplication on a C*-algebra A can be transposed to give a co-multiplication on the dual A*. Of course, this can be regarded as a special case of the preceding question by taking M = A**, where the double dual A** is identified with the enveloping von Neumann algebra of A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 5 , 01 October 1985 , pp. 769 - 784
Copyright
Copyright © Canadian Mathematical Society 1985

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