Normal Extensions Escape from the Class of Weighted Shifts on Directed Trees
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A formally normal weighted shift on a directed tree is shown to be a bounded normal operator. The question of whether a normal extension of a subnormal weighted shift on a directed tree can be modeled as a weighted shift on some, possibly different, directed tree is answered.
KeywordsDirected tree Weighted shift on a directed tree Formally normal operator Normal operator Subnormal operator
Mathematics Subject Classification (2010)Primary 47B15 47B37 Secondary 47B20
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