119 research outputs found
Composition operators on Hilbert spaces of entire functions with analytic symbols
Composition operators with analytic symbols on some reproducing kernel
Hilbert spaces of entire functions on a complex Hilbert space are studied. The
questions of their boundedness, seminormality and positivity are investigated.
It is proved that if such an operator is bounded, then its symbol is a
polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type
model for composition operators with linear symbols is established. As a
consequence, explicit formulas for their polar decomposition, Aluthge transform
and powers with positive real exponents are provided. The theorem of Carswell,
MacCluer and Schuster is generalized to the case of Segal-Bargmann spaces of
infinite order. Some related questions are also discussed.Comment: This is a final version of our previous submissions. It consists of
48 page
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
On th roots of bounded and unbounded quasinormal operators
In this paper, we prove that both hyponormal th roots of bounded
quasinormal and subnormal th roots of unbounded quasinormal operators are
quasinormal
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