Quanlei Fang

Multipliers and essential norm on the Drury-Arveson space

It is well known that for multipliers f of the Drury-Arveson space H 2 n , ∥f∥ ∞ does not dominate the operator norm of M f . We show that in general ∥f∥ ∞ does not even dominate the essential norm of M f . A consequence of this is that there exist multipliers f of H 2 n for which M f fails to be essentially hyponormal; i.e., if K is any compact, self-adjoint operator, then the inequality M* f M f - M f M* f + K ≥ 0 does not hold.