On Fixed Points for Semi-groups of Linear Operators
نویسنده
چکیده
That such theorems, when applied to the space X of bounded functions on a set S, have measure-theoretic significance was noted in [3]. Let 77 be a semi-group of 1-1 transformations of S into S. To each a EH we correspond the transformation T, of X into itself where T„(f) is the function f(a(s)), sES,fEX. These transformations form a semi-group G each element of which has norm one. Furthermore G has the unit function as a nonzero fixed point. If G* also possesses a nonzero fixed point x*, then there is a bounded additive set function p defined for all subsets of 5 such that
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