INVERSE PROBLEM ON ISOMORPHISM THEOREM OF A^{p}(G)$-ALGEBRAS ${1}le{p}le{2} (Nonlinear Analysis and Convex Analysis)

Abstract

Let G_{1} and G_{2} be locally compact Hausdorff groups, E(G_{1}) and E(G_{2}) the function spaces (Banach algebras or Banach spaces) on G_{1} and G_{2} respectively. Then it is known that if G_{1}simeq G_{2}, implies E(G_{1}) and E(G_{2}) are isomorphic. Naturally, an inverse problem arises that (P) Whether an algebaic isomorphism $Phi$ : E(G_{1})rightarrow E(G_{2}) could deduce G_{1}simeq G_{2}? In this paper, we would solve Problem (P) for A^{p}(G)-algebras, 1leq pleq 2.