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arXiv · 2506.14410

Surjective and closed range differentiation operator

Tesfa Mengestie
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Abstract

We identify Fock-type spaces $\mathcal{F}_{(m,p)}$ on which the differentiation operator $D$ has closed range. We prove that $D$ has closed range only if it is surjective, and this happens if and only if $m=1$. Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition--differentiation operator, $D_{(u,\psi,n)} f= u\cdot\big( f^{(n)}\circ \psi\big)$, on these spaces and describe conditions under which the operator admits closed range, surjective, and order bounded structures.

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Tesfa Mengestie. 2025-06-17. Surjective and closed range differentiation operator. https://doi.org/10.1007/s12215-024-01026-2

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