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Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2‐Spaces with Nondensely Defined Powers

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Listed:
  • Piotr Budzyński
  • Piotr Dymek
  • Zenon Jan Jabłoński
  • Jan Stochel

Abstract

It is shown that for every positive integer n there exists a subnormal weighted shift on a directed tree (with or without root) whose nth power is densely defined while its (n + 1)th power is not. As a consequence, for every positive integer n there exists a nonsymmetric subnormal composition operator C in an L2‐space over a σ‐finite measure space such that Cn is densely defined and Cn+1 is not.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:791817
DOI: 10.1155/2014/791817
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