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Closed range weighted composition operators between lp-spaces

Lo Ching-on, Wai-keung Loh Anthony

Opuscula Mathematica

2021

Vol. 41, no. 5

649--665

We characterize the closedness of ranges of weighted composition operators between Lp-spaces, where 1 <≤ p ≤ ∞. When the Lp-spaces are weighted sequence spaces, several corollaries about this class of operators are also deduced.

Weighted composition operators from weighted hardy spaces to weighted-type spaces

Zhu X.

Demonstratio Mathematica

2013

Vol. 46, nr 2

335--344

The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.

Injective composition operators on Lorentz-Bochner spaces

Datt G., Arora S. C.

Demonstratio Mathematica

2013

Vol. 46, nr 4

741--756

In this paper, we extend the notion of essential range to vector-valued functions and present various equivalent conditions for the injectiveness of the composition operators alongwith a characterisation for measurable transformations inducing composition operators between Lorentz-Bochner spaces. Some aspects of the weighted composition operators on Lorentz-Bochner spaces, induced by a measurable transformation and an operator valued map, are also discussed.

Weighted composition operators via Berezin transform and Carleson measure

Kumar R., Singh K. J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

63-78

In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in C^n.