We provide a version of the classical result of Kowalski and Slodkowski that generalizes the famous Gleason-Kahane-Zelazko (GKZ) theorem by characterizing multiplicative linear functionals amongst all complex-valued functions on a Banach algebra. We first characterize maps on A-valued polynomials of several variables that satisfy some conditions, motivated by the result of Kowalski and Slodkowski, as a composition of a multiplicative linear functional on A and a point evaluation on the polynomials, where A is a complex Banach algebra with identity. We then apply it to prove an analog of Kowalski and Slodkowski's result on topological spaces of vector-valued functions of several variables. These results extend our previous work from [3]; however, the techniques used differ from those used in [3]. Furthermore, we characterize weighted composition operators between Hardy spaces over the polydisc amongst the continuous functions between them. Additionally, we register a partial but noteworthy success toward a multiplicative GKZ theorem for Hardy spaces.

The authors sincerely thank the referee for their thorough review and constructive comments, which have greatly improved both the clarity and presentation of the paper. We thank the Mathematical Sciences Foundation, Delhi, for the support and facilities needed to complete the present work. The first named author thanks the University Grants Commission(UGC), India, for the support, and the second named author thanks Shiv Nadar Institution of Eminence for partially supporting this research.