The Russo-Dye Theorem in a weakly closed 𝒯(𝒩)–module

Abstract

Suppose that N \mathcal {N} is admissible. It is shown that the convex hull of unitary elements of a weakly closed T ( N ) \mathcal {T(N)} –module U \mathcal {U} contains the whole unit ball of U \mathcal {U} if and only if I ~ = I \widetilde {I}=I and for any N > 0 N>0 , N ~ > 0 \widetilde N>0 .