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PreprintCC BY 4.0arXiv

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∈ ℤgeqslant 4.

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Cite

BibTeXRIS
BibTeX
@misc{kujur2026woldtype,
  title = {{Wold-type decompositions for norm-increasing $m$-concave weighted shifts on directed trees}},
  author = {Ashish Kujur},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14662},
  eprint = {2609.14662},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14662},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Wold-type decompositions for norm-increasing m-concave weighted shifts on directed trees
AU  - Ashish Kujur
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14662
UR  - https://arxiv.org/abs/2609.14662
AB  - 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∈ ℤ_geqslant 4.
ER  -