Boundaries for Gelfand transform images of Banach algebras of holomorphic functions - Choi, Yun Sung; Jung, Mingu (MATHEMATICA SCANDINAVICA, 2023)
In this paper, we study boundaries for the Gelfand transform image of infinite dimensional analogues of the classical disk algebras. More precisely, given a certain Banach algebra A of bounded holomorphic functions on the open unit ball B_X of a complex Banach space X, we show that the Shilov boundary for the Gelfand transform image of A can be explicitly described for a large class of Banach spaces. Some possible application of our result to the famous Corona theorem is also briefly discussed.