Structural Properties of Homomorphism Dilation Systems

Chinese Annals of Mathematics, Series B - Tập 41 Số 4 - Trang 585-600 - 2020
Han, Deguang1, Larson, David R.2, Liu, Bei3, Liu, Rui4
1Department of Mathematics, University of Central Florida, Orlando, USA
2Department of Mathematics, Texas A&M University, College Station, USA
3School of Science, Tianjin University of Technology, Tianjin, China
4School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China

Tóm tắt

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.

Tài liệu tham khảo

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