On the Multiplication Operators from the Natural μ-Bloch-Type Space into Another Natural ω-Bloch-Type Space

This paper investigates the boundedness of multiplication operators Mψ between natural μ-Bloch-type spaces Bμ,nat(BX) (or their little μ-Bloch counterparts) and natural ω-Bloch-type spaces Bω,nat(BX) on the unit ball BX of a complex Banach space X. We establish complete characterizations for the boundedness of Mψ under varying conditions on the weight functions μ and ω, including specific cases such as logarithmic and power-weighted Bloch spaces. The results extend classical operator theory to infinite-dimensional settings, unifying prior work on finite-dimensional domains.