5 research outputs found
Unbounded quasinormal operators revisited
Various characterizations of unbounded closed densely defined operators
commuting with the spectral measures of their moduli are established.In
particular, Kaufman's definition of an unbounded quasinormal operator is shown
to coincide with that given by the third-named author and Szafraniec. Examples
demonstrating the sharpness of results are constructed.Comment: 13 page
Unbounded subnormal weighted shifts on directed trees
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.Comment: 32 pages, one figur