Maps preserving numerical radius and cross norms of operator products

摘要

Let H be a complex Hilbert space with dim H__3 and W, V __ B(H) be subsets that contain all rank-one idempotents. Let F(_) stand for numerical radius w(_) or a cross operator norm N(_). All the general surjective maps (1): W_ú V satisfying F(AB) = F(___)(A)__(B)) (resp., F(ABA) = F(__)(A)__(B)__(A))) for all A, B__ W are characterized.