Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-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 operator...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/791817 |
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| _version_ | 1849307191478059008 |
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| author | Piotr Budzyński Piotr Dymek Zenon Jan Jabłoński Jan Stochel |
| author_facet | Piotr Budzyński Piotr Dymek Zenon Jan Jabłoński Jan Stochel |
| author_sort | Piotr Budzyński |
| collection | DOAJ |
| description | 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 L2-space over a σ-finite measure space such that Cn is densely defined and Cn+1 is not. |
| format | Article |
| id | doaj-art-1bb5a3b54fd3460c8b1ae6ce2cefae62 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1bb5a3b54fd3460c8b1ae6ce2cefae622025-08-20T03:54:51ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/791817791817Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined PowersPiotr Budzyński0Piotr Dymek1Zenon Jan Jabłoński2Jan Stochel3Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Ulica Balicka 253c, 30-198 Kraków, PolandKatedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Ulica Balicka 253c, 30-198 Kraków, PolandInstytut Matematyki, Uniwersytet Jagielloński, Ulica Łojasiewicza 6, 30-348 Kraków, PolandInstytut Matematyki, Uniwersytet Jagielloński, Ulica Łojasiewicza 6, 30-348 Kraków, PolandIt 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 L2-space over a σ-finite measure space such that Cn is densely defined and Cn+1 is not.http://dx.doi.org/10.1155/2014/791817 |
| spellingShingle | Piotr Budzyński Piotr Dymek Zenon Jan Jabłoński Jan Stochel Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers Abstract and Applied Analysis |
| title | Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers |
| title_full | Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers |
| title_fullStr | Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers |
| title_full_unstemmed | Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers |
| title_short | Subnormal Weighted Shifts on Directed Trees and Composition Operators in L2-Spaces with Nondensely Defined Powers |
| title_sort | subnormal weighted shifts on directed trees and composition operators in l2 spaces with nondensely defined powers |
| url | http://dx.doi.org/10.1155/2014/791817 |
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