  Hartshorne's conjecture about vector bundles on projective space states that
any rank 2 vector bundle on n-dimensional projective space splits as soon as n
is at least 7. Klyachko has shown that Hartshorne's conjecture is true when the
vector bundles are torus equivariant. Moreover, recent work of Ilten and S\"uss
generalizes Klyachko's work to the case of a smaller rank torus action on
projective space. In this note we give a new, direct proof that torus rank 2
bundles split that avoids a description of the category of torus equivariant
vector bundles.
