In this work, we present necessary and sufficient conditions for compactness of the composition operator on Orlicz–Lorentz spaces and determine upper and lower estimates for the essential norm of the composition operator on these spaces.

In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.

In this paper, we study the boundedness of weighted composition operators between two Lp-spaces. We present equivalent conditions for the compactness of weighted composition operators between two Lp-spaces. We also give equivalent conditions for weighted composition operators with closed range.

In this paper, we study the boundedness and the compactness of composition operators on Orlicz–Lorentz spaces.

In this paper, we study weighted composition operators on Lp-spaces with finite ascent and descent. We also characterize the injective weighted composition operators.

In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.

We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a σ \sigma –finite measure space, Lorentz function spaces on a σ \sigma –finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.

We give a necessary and sufficient condition for the compactness of composition operators on the Lorentz spaces.