Projective Freeness of Algebras of Bounded Holomorphic Functions on Infinitely Connected Domains

2019/05/04 by Alexander Brudnyi, Brudnyi, A. · 1 citation
Mathematics · #Holomorphic and Operator Theory #Analytic and geometric function theory #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1905.01532

Abstract

The algebra H^∞(D) of bounded holomorphic functions on D⊂\mathbb C is projective free for a wide class of infinitely connected domains. In particular, for such D every rectangular left-invertible matrix with entries in H^∞(D) can be extended in this class of matrices to an invertible square matrix (the generalization of the corona theorem for H^∞(D)). This follows from a new result on the structure of the maximal ideal space of H^∞(D) asserting that its covering dimension is 2 and the second Čech cohomology group is trivial.

Cited by

• On Stable Rank of \mathbf H^∞ on Coverings of Finite Bordered Riemann Surfaces

Related

• Topology of the Maximal Ideal Space of H^∞
• Projective freeness and Hermiteness of complex function algebras
• Banach-valued Holomorphic Functions on the Maximal Ideal Space of H^∞
• A Uniqueness Property for H^∞ on Coverings of Projective Manifolds
• Another proof of the corona theorem