On fixed points for semi-groups of linear operators

On Fixed Points for Semi-groups of Linear Operators

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...

Semi-groups of Operators

Homotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups

If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z is Map∗(EK+, Z) K , the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X is often given by (HG,X), where HG,X is a certain explicit construction given by a homotopy limit in the category of discrete G-spectra. Thus, in each of two common equi...

Fixed Points of Finite Groups Acting on Generalised Thompson Groups

We study centralisers of finite order automorphisms of the generalised Thompson groups Fn,∞ and conjugacy classes of finite subgroups in finite extensions of Fn,∞. In particular we show that centralisers of finite automorphisms in Fn,∞ are either of type FP∞ or not finitely generated. As an application we deduce the following result about the Bredon type of such finite extensions: any finite ex...

A Note on Perturbation Theory for Semi-groups of Operators

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