Vector spaces with an order unitReport as inadecuate



 Vector spaces with an order unit


Vector spaces with an order unit - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: Vector spaces with an order unit
We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order seminorm on the space of self-adjoint elements admits multiple extensions to an order seminorm on the entire space. We single out three of these seminorms for further study and discuss their significance for operator algebras and operator systems. In addition, we introduce a functorial method for taking an ordered space with an order unit and forming an Archimedean ordered space. We then use this process to describe an appropriate notion of quotients in the category of Archimedean ordered spaces.



Author: Vern Paulsen; Mark Tomforde

Source: https://archive.org/







Related documents