Taiwanese Journal of Mathematics

Unified Approach to Spectral Properties of Multipliers

Mikael Lindström, Santeri Miihkinen, and David Norrbo

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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.

Article information

Taiwanese J. Math., Advance publication (2020), 25 pages.

First available in Project Euclid: 24 February 2020

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Digital Object Identifier

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 47B38: Operators on function spaces (general)

spectrum essential spectrum Hardy-Sobolev spaces Bergman-Sobolev spaces multiplication operator


Lindström, Mikael; Miihkinen, Santeri; Norrbo, David. Unified Approach to Spectral Properties of Multipliers. Taiwanese J. Math., advance publication, 24 February 2020. doi:10.11650/tjm/200205. https://projecteuclid.org/euclid.twjm/1582513213

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