Operator norms on L(E) (Q1080150)

For any Banach space E, all Banach algebra norms on L(E) are equivalent to the given operator norm on L(E). The authors characterize when a Banach algebra norm p on L(E) is an operator norm for some (equivalent) norm on E. In particular, p is an operator norm if and only if it is minimal with resepct to the pointwise ordering on norms; this generalizes a known result for matrices. In fact, the results hold for any closed subalgebra of L(E) that contains the finite rank operators.