Weighted shifts on directed trees
 Author/Creator
 Jablónski, Zenon Jan, 1973
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, 2012, c2011.
 Physical description
 vii, 107 p. ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1017.
Access
Available online

Stacks

Unknown
QA3 .A57 NO.1017

Unknown
QA3 .A57 NO.1017
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Contributors
 Contributor
 Jung, Il Bong, 1954
 Stochel, Jan, 1951
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Introduction
 Prerequisites (directed trees, operator theory)
 Fundamental properties (an invitation to weighted shifts, unitary equivalence, circularity, adjoints and moduli, the polar decomposition, Fredholm directed trees)
 Inclusions of domains
 Hyponormality and cohyponormality
 Subnormality
 Complete hyperexpansivity
 Miscellanea (admissibility of assorted weighted shifts, phyponormality)
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Zenon Jan Jabłoński, Il Bong Jung, Jan Stochel.
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1017
 Note
 "Volume 216, number 1017 (third of 4 numbers)."
 ISBN
 9780821868683
 0821868683