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

Published 8 Dec 2022 in math.FA | (2212.04446v3)

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 $2.$

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