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arXiv · 2602.15713

On the minimum modulus of dual truncated Toeplitz operators

Sudip Ranjan Bhuia·Ramesh Golla·Puspendu Nag
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Abstract

This article provides a systematic investigation of the minimum modulus of dual truncated Toeplitz operators (DTTOs) $D_{\varphi}$ acting on the orthogonal complement of the model space $\mathcal{K}_u^{\perp}$, where $u$ is a nonconstant inner function and $\varphi \in L^\infty(\T)$. We first establish an explicit formula for the minimum modulus of the compressed shift $S_u$ and its dual $D_u$ in terms of $|u(0)|$, and prove that the minimum is always attained. For normal DTTOs, we derive sharp spectral bounds utilizing the essential range of the symbol and characterize the conditions under which $m(D_{\varphi})$ coincides with the essential infimum of $|\varphi|$. In the general setting, for unimodular $\vp$, we obtain exact formulas and two sided estimates for $m(D_{\varphi})$ by analyzing the norms of associated Toeplitz and Hankel operators restricted to the model space. Finally, we provide several concrete examples to illustrate our results.

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Sudip Ranjan Bhuia, Ramesh Golla, Puspendu Nag. 2026-02-17. On the minimum modulus of dual truncated Toeplitz operators. https://arxiv.org/abs/2602.15713

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