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

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 oper...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.404-409-1339
Main Authors: Budzyński, Piotr, Dymek, Piotr, Jabłoński, Zenon Jan, Stochel, Jan
Format: Article
Language:English
Subjects:
Hilbert space
Integers
Operators
Roots
Trees
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Summary: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 L 2-space over a σ-finite measure space such that Cn is densely defined and C n + 1 is not.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/791817