Geodesic
Approximately Periodic Functionals on C*-Algebras and von Neumann Algebras
Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 769-784

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Quigg, John C. Approximately Periodic Functionals on C*-Algebras and von Neumann Algebras. Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 769-784. doi: 10.4153/CJM-1985-043-9
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