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Weighted Shifts on Directed Trees
Zenon Jan Jabłoński, Uniwersytet Jagielloński, Krakow, Poland, Il Bong Jung, Kyungpook National University, Daegu, South Korea, and Jan Stochel, Uniwersytet Jagielloński, Krakow, Poland

Memoirs of the American Mathematical Society
2012; 107 pp; softcover
Volume: 216
ISBN-10: 0-8218-6868-3
ISBN-13: 978-0-8218-6868-3
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/216/1017
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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
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