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arXiv · 1506.00163

On Toeplitz operators between Fock spaces

Tesfa Mengestie
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Abstract

We study mapping properties of Toeplitz operators $T_μ$ associated to nonnegative Borel measure $μ$ on the complex space $\mathbb{C}^n$. We, in particular, describe the bounded and compact operators $T_μ$ acting between Fock spaces in terms of the objects $t$-Berezin transforms, averaging functions, and averaging sequences of their inducing measures $μ$. An asymptotic estimate for the norms of the operators has been also obtained. The results obtained extend a recent work of Z. Hu and X. Lv and fills the remaining gap when both the smallest and largest Banach--Fock spaces are taken into account.

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Tesfa Mengestie. 2015-05-30. On Toeplitz operators between Fock spaces. https://arxiv.org/abs/1506.00163

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