Unbounded subnormal weighted shifts on directed trees. II

TL;DR

This paper develops criteria for determining when unbounded weighted shifts on directed trees are subnormal, focusing on trees with a single branching point, and explores classical cases and inductive limit methods.

Contribution

It introduces new criteria for subnormality of unbounded weighted shifts on directed trees, emphasizing the inductive limit approach and extending classical weighted shift analysis.

Findings

Criteria for subnormality of unbounded shifts on directed trees.

Relevance of inductive limit approach to subnormality.

Discussion of classical weighted shifts within this framework.

Abstract

Criteria for subnormality of unbounded injective weighted shifts on leafless directed trees with one branching vertex are proposed. The case of classical weighted shifts is discussed. The relevance of an inductive limit approach to subnormality of weighted shifts on directed trees is revealed.