The structure of Banach algebras of bounded continuous functions on the open disk that contain H∞, the Hoffman algebra, and nontangential limits
Abstract
Representable in the form HB⋂G, where G=C(M(H∞))def=alg(H∞,¯H∞) and HB is a closed subalgebra in C(D) consisting of the functions that have nontangential limits almost everywhere on T, and these limits belong to the Douglas algebra B. In this paper we describe the space M(HGB) of maximal ideals of the algebra HGB and prove that M(HGB)=M(B)⋃M(HG0) and prove that M(HG0), where HG0 is a closed ideal in G consisting of functions having nontangential limits equal to zero almost everywhere on T. Moreover, it is established that H∞⊃[¯Z]≠HGH∞+C on the disk. The Chang-Marshall theorem is generalized for the Banach algebras HGB. We also prove that HGB=alg(HGH∞,¯IB) for any Douglas algebra B, where IB={uα}B are inner functions such that ¯uα∈B on T.Published
25.07.1993
Issue
Section
Research articles
How to Cite
Ivanov, O. V. “The Structure of Banach Algebras of Bounded Continuous Functions on the Open Disk That Contain H∞, the Hoffman Algebra, and Nontangential Limits”. Ukrains’kyi Matematychnyi Zhurnal, vol. 45, no. 7, July 1993, pp. 924–931, https://umj.imath.kiev.ua/index.php/umj/article/view/5885.