Operator norms on L(E)
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.
minimal with resepct to the pointwise ordering on norms
scientific article; zbMATH DE number 3967208