Weighted Composition Operators That Preserve Frames On Weighted Hardy Spaces

Abstract

In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted composition operators. Moreover, we establish the equivalence between bounded invertible operators and frame-preserving operators. Furthermore, we show that weighted composition operator preserves frames if and only if it preserves the Riesz bases property. Additionally, we investigate the weighted composition operators that preserve tight or normalized tight frames on the Dirichlet space.