TY - JOUR
AU - Choi, Yun Sung
AU - Jung, Mingu
PY - 2023/02/20
Y2 - 2023/03/25
TI - Boundaries for Gelfand transform images of Banach algebras of holomorphic functions
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 129
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-134348
UR - https://www.mscand.dk/article/view/134348
SP -
AB - <p>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 $\mathcal{A}$ 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 $\mathcal{A}$ 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.</p>
ER -