Structural Properties of Homomorphism Dilation Systems
Deguang Han , David R. Larson , Bei Liu , Rui Liu
Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (4) : 585 -600.
Structural Properties of Homomorphism Dilation Systems
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.
Linear systems / Linearly minimal homomorphism dilation systems / Principle and universal dilations / Equivalent dilation systems
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