Operator norm inequalities of Minkowski type.
Operators of the q-oscillator
We scrutinize the possibility of extending the result of [19] to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it...
Operators with absolute continuity properties: an application to quasinormality
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.
Powers of class operators.
Powers of -hyponormal operators.
Proper contractions and invariant subspaces.
Quasinormal operators are hyperreflexive
We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.
Quasinormality and numerical ranges of certain classes of dual Toeplitz operators.
Quasireducible operators.
Reduced Cowen sets.
Selfadjoint operator matrices with finite rows
A generalization of the Carleman criterion for selfadjointness of Jacobi matrices to the case of symmetric matrices with finite rows is established. In particular, a new proof of the Carleman criterion is found. An extension of Jørgensen's criterion for selfadjointness of symmetric operators with "almost invariant" subspaces is obtained. Some applications to hyponormal weighted shifts are given.
Self-dual subnormal operators
Singular integral models for p-hyponormal operators and the Riemann-Hilbert problem
The purpose of this paper is to give singular integral models for p-hyponormal operators and apply them to the Riemann-Hilbert problem.
Some applications of functions of several complex variables to Toeplitz and subnormal operators
Some Berezin number inequalities for operator matrices
Some classes of commuting n-tuples of operators
Some estimates of certain subnormal and hyponormal derivations.
Some examples on lifting the commutant of a subnormal operator
Some invariant subspaces for A-contractions and applications
Some invariant subspaces for the operators A and T acting on a Hilbert space H and satisfying T*AT ≤ A and A ≥ 0, are presented. Especially, the largest invariant subspace for A and T on which the equality T* AT = A occurs, is studied in connections to others invariant or reducing subspaces for A, or T. Such subspaces are related to the asymptotic form of the subspace quoted above, this form being obtained using the operator limit of the sequence {T*nATn; n ≥ 1}. More complete results are given...
Some locally mean ergodic theorems
The notion of local mean ergodicity is introduced. Some general locally mean ergodic theorems for linear and affine operators are presented. Locally mean ergodic theorems for affine operators whose linear parts are compact or similar to subnormal operators on a Hilbert space are given.