Memoirs of the American Mathematical Society 2012; 107 pp; softcover Volume: 216 ISBN10: 0821868683 ISBN13: 9780821868683 List Price: US$70 Individual Members: US$42 Institutional Members: US$56 Order Code: MEMO/216/1017
 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. Table of Contents  Introduction
 Prerequisites
 Fundamental properties
 Inclusions of domains
 Hyponormality and cohyponormality
 Subnormality
 Complete hyperexpansivity
 Miscellanea
 Bibliography
 List of symbols
