Analytic $m$-isometries without the wandering subspace property
作者: Akash AnandSameer ChavanShailesh 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 propertyWold-type decompositionWeighted shiftOne-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...
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关键词翻译
关键词翻译
  • wandering 偏斜
  • subspace 子空间
  • directed 有[定,方]向
  • property 所有权
  • admit 容许
  • isometry 等距映射
  • invariant 不变量
  • analytic 解析的
  • shift 变位
  • dimensional 量纲的