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