On the algebra of bounded holomorphic martingales

Abstract

The properties of the algebra H ∞ {H^\infty } of bounded holomorphic martingales are further studied following the work of N. Th. Varopoulos [11]. The purpose of this paper is to discuss the behavior of weak* closed algebras B B with H ∞ ≠ ⊂ B ≠ ⊂ L ∞ {H^\infty }_ \ne ^ \subset B_ \ne ^ \subset {L^\infty } and the support sets of H ∞ {H^\infty } -functions. We also give some results on the factorization theorem for H ∞ {H^\infty } and extreme points of the unit ball of H ∞ {H^\infty } .