Subnormal Weighted Shifts on Directed Trees and Composition Operators inL2-Spaces with Nondensely Defined Powers-Reference-Cited by-同舟云学术

Subnormal Weighted Shifts on Directed Trees and Composition Operators inL2-Spaces with Nondensely Defined Powers

Published:2014 Issue: Volume:2014 Page:1-6
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Budzyński Piotr¹,Dymek Piotr¹²,Jabłoński Zenon Jan²,Stochel Jan²

Affiliation:

1. Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Ulica Balicka 253c, 30-198 Kraków, Poland

2. Instytut Matematyki, Uniwersytet Jagielloński, Ulica Łojasiewicza 6, 30-348 Kraków, Poland

Abstract

It is shown that for every positive integernthere exists a subnormal weighted shift on a directed tree (with or without root) whosenth power is densely defined while its (n+1)th power is not. As a consequence, for every positive integernthere exists a nonsymmetric subnormal composition operatorCin anL2-space over aσ-finite measure space such thatCnis densely defined andCn+1is not.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/791817.pdf

Reference23 articles.

1. On a class of operators

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1. Weighted shifts on directed trees: their multiplier algebras, reflexivity and decompositions;Studia Mathematica;2019

2. A Subnormal Completion Problem for Weighted Shifts on Directed Trees;Integral Equations and Operator Theory;2018-11-16

3. Quasinormal extensions of subnormal operator-weighted composition operators in ℓ2-spaces;Journal of Mathematical Analysis and Applications;2017-08

4. Subnormality of unbounded composition operators over one-circuit directed graphs: Exotic examples;Advances in Mathematics;2017-04

5. Analytic structure of weighted shifts on directed trees;Mathematische Nachrichten;2016-12-08