Unbounded subnormal weighted shifts on directed trees

Details Unbounded subnormal weighted shifts on directed trees Unbounded subnormal weighted shifts on directed trees

2011-05-18

arxiv.org/abs/1105.3641v1

Mathematics

Functional Analysis

32 pages, one figure

Scientific paper

A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established. An approach to this issue via consistent systems of probability measures is invented. The role played by determinate Stieltjes moment sequences is elucidated. Lambert's characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi-analytic vectors, which is a new phenomenon in this area. The cases of classical weighted shifts and weighted shifts on leafless directed trees with one branching vertex are studied.

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