Orthogonally Additive and Multiplicative Polynomials and Holomorphic Maps Between Fourier Algebras

Orthogonally additive polynomials on convolution algebras associated with a compact group

“…It is well-known that the Banach spaces A(G) and A p (G) of Example 6.3 are particularly important Banach function algebras with respect to the pointwise multiplication. We emphasize that while the references [1,2,14,15,16] apply to the problem of representing the orthogonally additive homogeneous polynomials on the Banach function algebras A(G) and A p (G) with respect to pointwise multiplication, Theorem 6.2 gives us information about that problem in the case where both A(G) and A p (G) are regarded as noncommutative Banach algebras with respect to convolution. Remark 6.6.…”

“…It is shown in [11] that the answer to Question Q2 is positive in the case where A is a C * -algebra (see [9,12] for the case where A is a C * -algebra and P is a holomorphic map). The references [1,2,14,15,16] discuss Question Q2 for a variety of Banach function algebras, including the Fourier algebra A(G) and the Figà-Talamanca-Herz algebra A p (G) of a locally compact group G.…”