Multipliers and Essential Norm on the Drury-arveson Space
نویسندگان
چکیده
It is well known that for multipliers f of the Drury-Arveson space H n, ‖f‖∞ does not dominate the operator norm of Mf . We show that in general ‖f‖∞ does not even dominate the essential norm of Mf . A consequence of this is that there exist multipliers f of H n for which Mf fails to be essentially hyponormal, i.e., if K is any compact, self-adjoint operator, then the inequality M∗ f Mf −MfM f + K ≥ 0 does not hold.
منابع مشابه
On the Problem of Characterizing Multipliers for the Drury-arveson Space
Let H n be the Drury-Arveson space on the unit ball B in C , and suppose that n ≥ 2. Let kz, z ∈ B, be the normalized reproducing kernel for H n. In this paper we consider the following rather basic question in the theory of the Drury-Arveson space: For f ∈ H n, does the condition sup|z|<1 ‖fkz‖ < ∞ imply that f is a multiplier of H n? We show that the answer is negative. We further show that t...
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