Geodesic
Norm Decreasing Homomorphisms Between Ideals of Lp (G)
Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 102-111

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

Let G1 and G 2 be compact groups and T : Lp(G1) → LP(G2) (1 ≦ P ≦ ∞ ) be an algebra homomorphism. If || T || ≦ 1 and T is either a monomorphism of an epimorphism then T can in many cases be explicitly characterized (see [4 ; 8 ; 9 ; 11 ; 13 ; 14]). Excluding p = 2, the outstanding cases are 1 < p < ∞ for monomorphisms and 2 < p < ∞ for epimorphisms (cf. [14]). One aim of the present note is to complete this work. We also consider the problem of extending these results in some form to homomorphisms on ideals of group algebras; the only known result in this area is for abelian groups [3]. 
Kalton, N. J.; Wood, G. V. Norm Decreasing Homomorphisms Between Ideals of Lp (G). Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 102-111. doi: 10.4153/CJM-1978-009-0
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