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December, 2020 Unified Approach to Spectral Properties of Multipliers
Mikael Lindström, Santeri Miihkinen, David Norrbo
Taiwanese J. Math. 24(6): 1471-1495 (December, 2020). DOI: 10.11650/tjm/200205


Let $\mathbb{B}_n$ be the open unit ball in $\mathbb{C}^n$. 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 $A^p_{\alpha,\beta}$, Bloch-type spaces $\mathcal{B}_{\alpha}$, weighted Hardy spaces $H^p_w$ with Muckenhoupt weights and Hardy-Sobolev Hilbert spaces $H^2_{\beta}$. 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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Mikael Lindström. Santeri Miihkinen. David Norrbo. "Unified Approach to Spectral Properties of Multipliers." Taiwanese J. Math. 24 (6) 1471 - 1495, December, 2020.


Received: 11 December 2019; Accepted: 16 February 2020; Published: December, 2020
First available in Project Euclid: 19 November 2020

MathSciNet: MR4176883
Digital Object Identifier: 10.11650/tjm/200205

Primary: 47B35 , 47B38

Keywords: Bergman-Sobolev spaces , essential spectrum , Hardy-Sobolev spaces , multiplication operator , spectrum

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 6 • December, 2020
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