## Abstract and Applied Analysis

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

#### 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 L 2-space over a σ-finite measure space such that Cn is densely defined and ${C}^{n+1}$ is not.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 791817, 6 pages.

Dates
First available in Project Euclid: 7 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412687021

Digital Object Identifier
doi:10.1155/2014/791817

Mathematical Reviews number (MathSciNet)
MR3173291

Zentralblatt MATH identifier
1259.35155

#### Citation

Budzyński, Piotr; Dymek, Piotr; Jabłoński, Zenon Jan; Stochel, Jan. Subnormal Weighted Shifts on Directed Trees and Composition Operators in $L^2$&gt;-Spaces with Nondensely Defined Powers. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 791817, 6 pages. doi:10.1155/2014/791817. https://projecteuclid.org/euclid.aaa/1412687021

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