Subnormal weighted shifts on directed trees whose nth powers have trivial domain

2014/09/29 by Budzynski, Piotr, Jablonski, Zenon Jan, Jung, Il Bong +1
#47B37 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B20 #Secondary 47B33

paper · doi:10.48550/arxiv.1409.8022

Abstract

It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its (n + 1)th power has trivial domain. Similar result for composition operators in L2-spaces is established.

Related

• Subnormal weighted shifts on directed trees and composition operators in L² spaces with non-densely defined powers
• Unbounded subnormal weighted shifts on directed trees
• A hyponormal weighted shift on a directed tree whose square has trivial domain
• On complex symmetric weighted shifts. II
• Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions