Surjective norm-additive in modulus maps between real Lipschitz algebras with Lipschitz involution

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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

Language:
Persian
Published:
Journal of Mathematical Researches, Volume:10 Issue: 4, 2025
Pages:
77 to 99
https://www.magiran.com/p2834823  
سامانه نویسندگان
  • Davood Alimohammadi
    Corresponding Author (2)
    Associate Professor Department of Mathematics, Faculty of Science, Arak University, University Of Arak, Arak, Iran
    Alimohammadi، Davood
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