Unified approach to spectral properties of multipliers

2020/02/17 by Lindström, Mikael, Miihkinen, Santeri, Norrbo, David
#47B35 (Primary) #47B38 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2002.07035

Abstract

Let \mathbb B_n be the open unit ball in \mathbb Cⁿ. We characterize the spectra of pointwise multipliers M_u acting on Banach spaces of analytic functions on \mathbb B_n satisfying some general conditions. These spaces include Bergman-Sobolev spaces A^p_α,β, Bloch-type spaces \mathcal B_α, weighted Hardy spaces H^p_w with Muckenhoupt weights and Hardy-Sobolev Hilbert spaces H²_β. Moreover, we describe the essential spectra of multipliers in most of the aforementioned spaces, in particular, in those spaces for which the set of multipliers is a subset of the ball algebra.

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