A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.
| ISBN: | 9780821868683 |
| Publication date: | 30th March 2012 |
| Author: | Zenon Jan Jablónski, Il Bong Jung, Jan Stochel |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 107 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Calculus and mathematical analysis |