2021/04/02 by Mohammad Ali Ahmadpoor, Ahmadpoor, Mohammad Ali, Marzieh Shams Yousefi +1
Mathematics · #47L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Primary 46L07 #Secondary 43A30
paper · pdf · doi:10.48550/arxiv.2104.01171
openalex publication_date 2021/04/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper, for p∈(1,∞) we study p-complete boundedness of weighted homomorphisms on the p-analog of the Fourier-Stieltjes algebras, Bp(G), based on the p-operator space structure defined by the authors. Here, for a locally compact group G, the space Bp(G) stands for Runde's definition of the p-analog of the Fourier-Stieltjes algebra and the implemented p-operator space structure is come from the duality between Bp(G) and the algebra of universal p-pseudofunctions, UPFp(G). It is established that the homomorphism Φα:Bp(G)→ Bp(H), defined by Φ(u)=u∘α on Y and zero otherwise, is p-completely contractive when the continuous and proper map α:Y⊆ H→ G is affine, and it is p-completely bounded whenever α is piecewise affine map. Moreover, we assume that Y belongs to the coset ring generated by open and amenable subgroups of H. To obtain the result, by utilizing the properties of QSLp-spaces and representations on them, the relation between Bp(G/N) and a closed subalgebra of Bp(G) is shown, where N is a closed normal subgroup of G. Additionally, p-complete boundedness of several well-known maps on such algebras are obtained.