Subnormal Weighted Shifts on Directed Trees and Composition Operators in 2 -Spaces with Nondensely Defined Powers

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

Abstract and Applied Analysis, 2014, vol. 2014, 1-6

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 n th power is densely defined while its ( )th power is not. As a consequence, for every positive integer n there exists a nonsymmetric subnormal composition operator C in an L 2 -space over a σ -finite measure space such that C n is densely defined and is not.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:791817

DOI: 10.1155/2014/791817

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