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Extension of invariant linear functionals

Author: Ky Fan
Journal: Proc. Amer. Math. Soc. 66 (1977), 23-29
MSC: Primary 46A30; Secondary 47D05
MathSciNet review: 0458111
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Abstract: In a recent paper [4] we considered a semigroup of linear contractions or a group of linear isometries in a normed vector space, and obtained sufficient conditions for the orbits to lie on parallel closed hyperplanes. In the present note, we take a more general viewpoint and shall prove some theorems on extension of continuous linear functionals which are invariant under a group or a semigroup of continuous linear maps on a locally convex topological vector space. These more general results include those in [4] as direct consequences.

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