The authors study the finite decomposition complexity of metric spaces of H,equipped with different metrics,where is a subgroup of the linear group GL∞ (Z).It is proved that there is an injective Lipschitz mapφ:(F,ds) → (H,d),where is the Thompson's group,the word-metric of with respect to the finite generating set and a metric of H.But it is not a proper map.Meanwhile,it is proved that:φ(F,ds) → (H,d1) is not a Lipschitz map,where d1 is another metric of H.
In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indecomposable systems of n subspaces.
This paper generalizes the C*-dynamical system to the Banach algebra dynamical system(A,G,α)and define the crossed product A α G of a given Banach algebra dynamical system(A,G,α).Then the representation of A α G is described when A admits a bounded left approximate identity.In a natural way,the authors define the reduced crossed product A α,r G and discuss the question when A α G coincides with A α,r G.
