Weighted Composition Groups on the Little Bloch Space. (29th April 2020)

• Record Type: Journal Article
• Authors: Mose, S. B.; Bonyo, J. O.
• Other Names: Gheondea Aurelian Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-04-29
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/5480602
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We determine both the semigroup and spectral properties of a group of weighted composition operators on the little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. As a consequence, we complete the analysis of the adjoint composition group on the predual of the nonreflexive Bergman space and a group of isometries associated with a specific automorphism of the upper half-plane. Dedicated to Prof. Len Miller (PhD advisor to J. O. Bonyo) and Prof. Vivien Miller of Mississippi State University on their retirement