Geodesic
Locally convex group algebras over compact groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1019-1031.

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It is proved that Tannaka-Krein duality theorem can be formulated through mutually conjugated locally convex Hopf algebras constructed by the group algebra $\mathbb C[G]$ and the Krein algebra of representation functions. 
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S. A. Pyartli. Locally convex group algebras over compact groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1019-1031. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a11/

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