Antinormal composition operators on $ \mbf{\ell^2}$

Composition Operators and Multiplication Operators on Orlicz Spaces

This article has no abstract.

On reducibility of weighted composition operators

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

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

Composition Operators on Small Spaces

We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators on small spaces. ...

Compact composition operators on certain analytic Lipschitz spaces

We investigate compact composition operators on ceratin Lipschitzspaces of analytic functions on the closed unit disc of the plane.Our approach also leads to some results about compositionoperators on Zygmund type spaces.