James’ Theorem

“James’ Theorem: The result that a subset of a Banach space is compact in the weak topology if and only if it is weakly closed and every continuous linear functional achieves its supremum on the set. In particular, a Banach space is reflexive if and only if every continuous linear functional supports the unit ball at some point.” [From The Harper Collins Mathematics Dictionary, by Borowski & Borwein]

The aforementioned theorem has no connection whatsoever to this piece. James’ Theorem is dedicated to the ensemble Hemispheres, and to its director, Nic Gotham. It was commissioned by Hemispheres through The Ontario Arts Council.