Positive maps which are bijective on the set of rank projections

TL;DR

This paper characterizes positive maps on operator algebras that bijectively map rank k projections onto themselves, extending Wigner's theorem to a broader class of maps.

Contribution

It provides a new characterization of positive maps that preserve rank k projections, generalizing Wigner's theorem.

Findings

Characterization of positive maps preserving rank k projections

Extension of Wigner's theorem to new classes of maps

Insights into structure of positive maps on operator algebras

Abstract

Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.