Projective free algebras of bounded holomorphic functions on infinitely connected domains

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-06-27 DOI:10.1090/spmj/1718

A. Brudnyi

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引用次数: 2

Abstract

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

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无限连通域上有界全纯函数的射影自由代数

D⊂C D\subet \mathbb｛C｝上有界全纯函数的代数H∞（D）H^\infty（D）对于一大类无限连通域是无投影的。特别地，对于这样的D D，每一个在H∞（D）H^\infty（D）中有项的矩形左可逆矩阵都可以在这类矩阵中推广为可逆平方矩阵。这源于关于H∞（D）H^\infty（D）的最大理想空间结构的一个新结果，该结果断言其覆盖维数为2，并且第二Čech上同调群是平凡的。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.