Maps leaving functional values of operator products invariant

Let A be a standard operator algebra on a complex Hilbert space H of dimension greater than 2. By invariants of certain functional values of operator products, we characterize some surjective maps on A. Furthermore, several kinds of general preserver problems on standard operator algebras are solved when we take respectively the functional as, for example, k-numerical radius (k⩾1), operator norm, Ky Fan k-norm, Schatten p-norm (1⩽p<∞), and so on.