Corpus ID: 214728089

# The face generated by a point, generalized affine constraints, and quantum theory

@article{Weis2020TheFG,
title={The face generated by a point, generalized affine constraints, and quantum theory},
author={Stephan Weis and Maksim E. Shirokov},
journal={arXiv: Functional Analysis},
year={2020}
}
• Published 31 March 2020
• Mathematics, Physics
• arXiv: Functional Analysis
We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex set with a sublevel or level set of a generalized affine functional, the dimension of the face generated by a point may decrease by at most one. We apply the results to the set of quantum states on a separable Hilbert space. Among others, we show that every state having finite expected values of any two (not… Expand

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