Failure of the wandering subspace property for analytic norm-increasing
  $3$-isometries

doi:10.48550/arxiv.2212.04446

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Failure of the wandering subspace property for analytic norm-increasing $3$-isometries

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TLDR

In this article , an analytic norm-increasing $3$-isometric weighted shift on a rootless directed tree was constructed, which does not have the wandering subspace property.

Abstract:

We construct an analytic norm-increasing $3$-isometric weighted shift on a rootless directed tree, which does not have the wandering subspace property. This answers a question of Shimorin [S2001, p. 185] in the negative. The counterexample in question is built over the rootless quasi-Brownian directed tree of valency $2.$