The Topological Structure of Weighted Composition Operators from Lipschitz Spaces to H∞.

We give some simple norm estimates of the difference of weighted composition operators acting from Lipschitz space L α to the space H ∞ of all analytic functions on the unit disk, and showing that any two bounded weighted composition operators are pathwise connected. We also obtain some necessary or sufficient conditions for the difference to be compact. Unlike the equivalence of the boundedness and compactness for weighted composition operators from L α to H ∞ , we show that there exists a difference which is bounded, but not compact. [ABSTRACT FROM AUTHOR]
Copyright of Bulletin of the Malaysian Mathematical Sciences Society is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)