Subnormal generalized Hausdorff operators

Generalized Hausdorff Matrices as Bounded Operators on ! p*

Existence of Non-subnormal Polynomially Hyponormal Operators

In 1950, P. R. Halmos, motivated in part by the successful development of the theory of normal operators, introduced the notions of subnormality and hyponormality for (bounded) Hilbert space operators. An operator T is subnormal if it is the restriction of a normal operator to an invariant subspace; T is hyponormal if T*T > TT*. It is a simple matrix calculation to verify that subnormality impl...

Hyperinvariant Subspaces for Some Subnormal Operators

In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every “normalized” subnormal operator S such that either {(S∗nSn)1/n} does not converge in the SOT to the identity operator or {(SnS∗n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subsp...

Lifting strong commutants of unbounded subnormal operators

Various theorems on lifting strong commutants of unbounded sub-normal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operator S lifts to the strong commutant of some tight selfadjoint extension of S. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreduci...

Complex and Real Hausdorff Operators

Hausdorff operators (Hausdorff summability methods) appeared long ago aiming to solve certain classical problems in analysis. Modern theory of Hausdorff operators started with the work of Siskakis in complex analysis setting and with the work of Georgakis and Liflyand-Móricz in the Fourier transform setting. While Hausdorff operators for power series are still studied mostly in dimension one, t...