Banach-valued holomorphic functions on the maximal ideal space of H∞

• 成果类型: Article
• 署名作者: Brudnyi, Alexander
• 署名单位: University of Calgary
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0426-z
• 发表日期: 2013
• 页码: 187-227
• 关键词: bounded analytic-functions; corona theorem; projections

摘要

We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H (a) of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H (a), prove that the maximal ideal space of the algebra of holomorphic functions on with relatively compact images in a commutative unital complex Banach algebra A is homeomorphic to the direct product of maximal ideal spaces of H (a) and A.