Surjective norm-additive in modulus maps between real Lipschitz algebras with Lipschitz involution
Let (X‚ d) and (Y‚ ρ) be compact metric spaces‚ τ be a Lipschitz involution on (X‚ d) and η be Lipschitz involution on (Y‚ ρ). Suppose that for all x∈X‚ for all y∈Y‚ , A is a real subalgebra of C(X‚ τ) which contains Lip(X‚ d‚ τ) and B is a real subalgebra of C(Y‚ η) which contains Lip(Y‚ ρ‚ η). We prove that if T:A→B is a surjetive -homogenous norm-additive in modulus map then there exists a unique bijection such that for all f∈A ‚ y∈Y and . Applying this fact‚ we show that if (X‚d) and (Y‚ρ) are compact metric spaces and is a surjective -homogenous norm-additive in modulus map then there exists a Lipschitz homeomorphism from to such that for all and y∈Ỵ
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Weighted composition operators on extended analytic Lipschitz algebras
Rezvan Barzegari, *
International Journal Of Nonlinear Analysis And Applications, Aug 2025 -
Weakly compact weighted composition operators on pointed Lipschitz spaces
Rezvan Barzegari, *
Caspian Journal of Mathematical Sciences, Winter Spring 2024