Analytic $m$-isometries without the wandering subspace property
 作者： Akash Anand,  Sameer Chavan,  Shailesh Trivedi 刊名： Proceedings of the American Mathematical Society, 2020, Vol.148 (5), pp.2129-2142 来源数据库： American Mathematical Society Journal DOI： 10.1090/proc/14894 关键词： Wandering subspace property;  Wold-type decomposition;  Weighted shift;  One-circuit directed graphs; 原始语种摘要： The wandering subspace problem for an analytic norm-increasing $m$-isometry $T$ on a Hilbert space $\mathcal {H}$ asks whether every $T$-invariant subspace of $\mathcal {H}$ can be generated by a wandering subspace. An affirmative solution to this problem for $m=1$ is ascribed to Beurling-Lax-Halmos, while that for $m=2$ is due to Richter. In this paper, we capitalize on the idea of weighted shift on a one-circuit directed graph to construct a family of analytic cyclic $3$-isometries which do not admit the wandering subspace property and which are norm-increasing on the orthogonal complement of a one-dimensional space. Further, on this one-dimensional space, their norms can be made arbitrarily close to $1$. We also show that if the wandering subspace property fails for an... analytic norm-increasing $m$-isometry, then it fails miserably in the sense that the smallest $T$-invariant subspace generated by the wandering subspace is of infinite codimension.

• wandering　偏斜
• subspace　子空间
• directed　有[定，方]向
• property　所有权