Structural Properties of Homomorphism Dilation Systems  

作　　者：Deguang HAN David R.LARSON Bei LIU Rui LIU 

机构地区：[1]Department of Mathematics,University of Central Florida,Orlando 32816,USA. [2]Department of Mathematics,Texas A&M University,College Station 77843,USA. [3]School of Science,Tianjin University of Technology,Tianjin 300384,China. [4]Corresponding author.School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China.

出　　处：《Chinese Annals of Mathematics,Series B》2020年第4期585-600,共16页数学年刊（B辑英文版）

基　　金：the National Science Foundation(Nos.DMS-1403400,DMS-1712602);the National Natural Science Foundation of China(No.11671214);the Young Academia Leaders Program of Nankai University。

摘　　要：Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras,the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces.By introducing two natural dilation structures,namely the canonical and the universal dilation systems,they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation,and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation.

关 键 词：Linear systems Linearly minimal homomorphism dilation systems Principle and universal dilations Equivalent dilation systems 

分 类 号：O177[理学—数学]