Compact and Weighted Composition Operators on 𝝁-Bergman and Maeda-Ogasawara Spaces with Rigidity on Hardy Spaces

Abstract

It is shown that composition operators on the Bloch space in polydiscs and on 𝜇-Bloch type spaces are dealt with. The weighted composition operators between μ- Bloch spaces on the unit ball, of 𝐶0(𝑋) and on Maeda-Ogasawara spaces are considered. The compact and weakly compact operators on BMOA, on Bergman and μ-Bergman spaces in the unit ball are studied. In addition the isometries between function spaces, on Banach-Stone theorem, atomic decomposition of μ-Bergman spaces in unitary space and strict singularity of Volterra-type integral operator on Hardy space are characterized. We show the linear isometries spaces of Lipschitz and vector-valued Lipschitz functions. The new properties, approximation numbers and rigidity of composition operators are discussed.