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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 791817, 6 pages
http://dx.doi.org/10.1155/2014/791817
Research Article

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

1Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Ulica Balicka 253c, 30-198 Kraków, Poland
2Instytut Matematyki, Uniwersytet Jagielloński, Ulica Łojasiewicza 6, 30-348 Kraków, Poland

Received 15 October 2013; Accepted 3 December 2013; Published 19 February 2014

Academic Editor: Henryk Hudzik

Copyright © 2014 Piotr Budzyński et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 ( )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 is not.