非交换球子变量上的全态函数代数束

IF 0.6 4区 数学 Q3 MATHEMATICS
Maria Dmitrieva
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引用次数: 0

摘要

我们提出了在封闭非交换球的子变量上连续巴拿赫全形函数代数束的一般构造。这些代数是 \(\mathcal{A}_d/\overline{I_x}\) 形式的,其中 \(\mathcal{A}_d\) 是由 G. Popescu 定义的非交换圆盘代数。Popescu定义的非交换圆盘代数,而\(\overline{I_x}\)是非交换多项式代数中分级理想\(I_x\)在\(\mathcal{A}_d\)中的闭包,连续地依赖于拓扑空间\(X\)的点\(x\)。此外,我们还在开放非交换球的子变量上构造了全态函数的弗雷谢特代数束(\mathcal{F}_d/\overline{I_x}/)。波佩斯库(G. Popescu)也引入了单位球上自由全态函数的代数(\(\mathcal{F}_d\)),\(\overline{I_x}\)代表了非交换多项式代数中分级理想\(I_x\)在\(\mathcal{F}_d\)中的闭包,它连续地依赖于一个点\(x\in X\).
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bundles of Holomorphic Function Algebras on Subvarieties of the Noncommutative Ball

We suggest a general construction of continuous Banach bundles of holomorphic function algebras on subvarieties of the closed noncommutative ball. These algebras are of the form \(\mathcal{A}_d/\overline{I_x}\), where \(\mathcal{A}_d\) is the noncommutative disc algebra defined by G. Popescu, and \(\overline{I_x}\) is the closure in \(\mathcal{A}_d\) of a graded ideal \(I_x\) in the algebra of noncommutative polynomials, depending continuously on a point \(x\) of a topological space \(X\). Moreover, we construct bundles of Fréchet algebras \(\mathcal{F}_d/\overline{I_x}\) of holomorphic functions on subvarieties of the open noncommutative ball. The algebra \(\mathcal{F}_d\) of free holomorphic functions on the unit ball was also introduced by G. Popescu, and \(\overline{I_x}\) stands for the closure in \(\mathcal{F}_d\) of a graded ideal \(I_x\) in the algebra of noncommutative polynomials, depending continuously on a point \(x\in X\).

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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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