Work

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

Year: 2026

Type: preprint

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 $m\in \mathbb{Z}_{\geqslant 4}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.14662

Author: Kujur, Ashish

Institutions: Council for Scientific and Industrial Research, Indian Institute of Science Education and Research Thiruvananthapuram, Council of Scientific and Industrial Research

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213274650

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