Weighted Shifts on Directed Trees
Author： Zenon Jan Jabłoński;Il Bong Jung;Jan Stochel
Publisher： American Mathematical Society
Publication year： 2012
E-ISBN: 9780821885277
P-ISBN(Paperback): 9780821868683
P-ISBN(Hardback): 9780821868683
Subject： O177 functional analysis
Keyword： Analysis
Language： ENG
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Weighted Shifts on Directed Trees
Description
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.