Relating Operator Spaces via Adjunctions

Details Relating Operator Spaces via Adjunctions Relating Operator Spaces via Adjunctions

2012-01-05

arxiv.org/abs/1201.1272v1

Computer Science

Logic in Computer Science

Scientific paper

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various Hilbert-Schmidt isomorphisms of the form $\tr(A-)$, are expressed in terms of dual adjunctions, and maps between them. Of particular interest is the connection with quantum structures, via a dual adjunction between convex sets and effect modules. The approach systematically uses categories of modules, via their description as Eilenberg-Moore algebras of a monad.

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