On Toeplitz operators between Fock spaces

2015/05/30 by Mengestie, Tesfa · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1506.00163

Abstract

We study mapping properties of Toeplitz operators T_μ associated to nonnegative Borel measure μ on the complex space ℂⁿ. 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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