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Norm Decreasing Homomorphisms Between Ideals of Lp(G)

Published online by Cambridge University Press:  20 November 2018

N. J. Kalton  and
G. V. Wood
N. J. Kalton
Affiliation:
University College of Swansea, Swansea, U.K.SA2 8PP
G. V. Wood
Affiliation:
University College of Swansea, Swansea, U.K.SA2 8PP
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Let G1 and G2 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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 102 - 111
Copyright
Copyright © Canadian Mathematical Society 1978

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