On some automorphisms of the set of effects on Hilbert space
Lajos Molnar
TL;DR
This paper characterizes the automorphisms of the set of effects on a Hilbert space, exploring its affine and multiplicative structures, including the Jordan triple product.
Contribution
It provides a detailed description of the automorphisms of the effects set, highlighting the interplay of affine and multiplicative structures.
Findings
Automorphisms preserve the convex structure of effects.
Automorphisms respect the Jordan triple product.
The structure of automorphisms is fully characterized.
Abstract
The set of all efects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set.
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Taxonomy
TopicsMatrix Theory and Algorithms