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Let Bn be the unit ball of Cn and φ = (φ1, . . . , φn) a holomorphic self-map of Bn. Let 0 < p,s < ∞, −n−1 < q < ∞, q s > −1,α > 0, and let Cφ be the composition operator between the space F(p, q, s) and α-Bloch space Bα induced by φ. This paper gives an estimate of the essential norm of Cφ. As a consequence, a necessary and sufficient condition for the composition operator Cφ to be compact from F(p, q, s) to Bα is obtained. [ABSTRACT FROM AUTHOR]

We characterize the isometries on the products of composition and integral operators on the Bloch type space in the disk. [ABSTRACT FROM AUTHOR]

The article reports on the study of the spectrum structure of compact operators on Hardy spaces of a unit ball. It aims to determine the spectrum of compact operators in weighted hardy spaces of a unit ball through eigenvalues of the compact operators. It uses differential equations and different theorems of inequalities in analyzing the spectrum structure. It also shows that the spectral radius of compact operators are nonautomorphism linear fractional map which takes the unit sphere to an ellipsoid sphere.