Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces

“…Among the recent results related to multipliers, we would like to mention the following developments. Interpolation problems for multipliers and model theory related to the Drury-Arveson space have been intensely studied over the past decade or so [4,5,10,12]. Recently, Arcozzi, Rochberg and Sawyer gave a characterization of the multipliers in terms of Carleson measures for H 2 n [1].…”

Section: Introductionmentioning

confidence: 99%

Multipliers and essential norm on the Drury-Arveson space

Fang¹,

Xia²

2010

Proc. Amer. Math. Soc.

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Abstract. 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

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“…The commutant lifting theorem will be used to extend some algebraic results for the case of quotient modules of the DruryArveson module. The commutant lifting theorem for the Drury-Arveson module is due to Ball, Trent and Vinnikov, Theorem 5.1 in [BaTrVi01].…”

Section: Lifting and Range-inclusion Theoremsmentioning

confidence: 99%