Analytic structure in fibers of H-infinity(B-c0)

Abstract

Let H-infinity(B-c0) be the algebra of all bounded holomorphic functions on the open unit ball of c(0) and M(H-infinity(B-c0)) the spectrum of H-infinity(B-c0)). We prove that for any point z in the closed unit ball of l(infinity) there exists an analytic injection of the open ball B-l infinity into the fiber of z in M(H-infinity(B-c0)), which is an isometry from the Gleason metric of B(l infinity )to the Gleason metric of M(H-infinity(B-c0)). We also show that, for some Banach spaces X, B-l infinity can be analytically injected into the fiber M-z(H-infinity(B-c0)) for every point z is an element of B-X. (C) 2020 Elsevier Inc. All rights reserved.