A note on hyponormal weighted shifts

Quartically Hyponormal Weighted Shifts Need Not Be 3-hyponormal

We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal.

Propagation Phenomena for Hyponormal 2-variable Weighted Shifts

We study the class of hyponormal 2-variable weighted shifts with two consecutive equal weights in the weight sequence of one of the coordinate operators. We show that under natural assumptions on the coordinate operators, the presence of consecutive equal weights leads to horizontal or vertical flatness, in a way that resembles the situation for 1-variable weighted shifts. In 1variable, it is w...

A Note on Subnormal and Hyponormal Derivations

In this note we prove that if A and B∗ are subnormal operators and X is a bounded linear operator such that AX − XB is a Hilbert-Schmidt operator, then f(A)X −Xf(B) is also a Hilbert-Schmidt operator and ||f(A)X −Xf(B)||2 ≤ L ||AX −XB||2, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and X ∈ L(H) i...

A Note on (Cp,)-Hyponormal Operators

A Note on Weighted Composition Operators on L^p-Spaces