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

Piotr Budzyński, Piotr Dymek, Zenon Jan Jabłoński and Jan Stochel

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/791817

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:791817

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