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arXiv · 2609.14662

Wold-type decompositions for norm-increasing $m$-concave weighted shifts on directed trees

Ashish Kujur
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Abstract

In this article, we show that every norm-increasing $3$-concave weighted shift on a directed tree admits Wold-type decomposition. We then classify the $4$-isometries within a class of weighted shifts on a rootless directed tree introduced by S. Chavan and S. Trivedi, and use this classification to construct analytic norm-increasing strict $4$-isometries without the wandering subspace property. This answers a question of S. Shimorin in the negative for every $m\in \mathbb{Z}_{\geqslant 4}$.

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BibTeXRIS

Ashish Kujur. 2026-09-13. Wold-type decompositions for norm-increasing $m$-concave weighted shifts on directed trees. https://arxiv.org/abs/2609.14662

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