复椭球交点上Bergman模的基本正态性

IF 0.7 3区 数学 Q2 MATHEMATICS
M. Jabbari
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引用次数: 0

摘要

Hilbert空间H上的算子的交换元组(T1,…,Tm),也称为多算子,如果所有交换子[Tj,T*k],j,k=1,m是紧凑的。或者,本质正规性可以归属于由(T1,…,Tm)生成的Hilbert C[z1,…,zm]模,即H配备有由P(T1,..,Tm。Brown、Douglas和Fillmore[12,13,19]将本质上正规的多算子分类为酉等价。这里的完全分类器是从紧致可度量空间范畴到阿贝尔群范畴的奇K-同调函子K1。更准确地说,对于任何紧致子空间X⊆Cm,阿贝尔群K1(X)将具有本质泰勒谱X的本质正规多算子分类到酉等价;K1(X)的元素是从C(X)到模理想的H上有界算子代数的C*单态的等价类
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Essential normality of Bergman modules over intersections of complex ellipsoids
A commuting tuple (T1, . . . , Tm) of operators, also called a multioperator, on a Hilbert space H is called essentially normal if all of the commutators [Tj , T ∗ k ], j, k = 1, . . . ,m are compact. Alternatively, essential normality can be attributed to the Hilbert C[z1, . . . , zm]module generated by (T1, . . . , Tm), namely, H equipped with the module action P (z1, . . . , zm)· f , P ∈ C[z1, . . . , zm], f ∈ H given by P (T1, . . . , Tm)f . Brown, Douglas and Fillmore [12, 13, 19] classified essentially normal multioperators up to unitary equivalence. The complete classifier here is the odd K-homology functor K1 from the category of compact metrizable spaces to the category of abelian groups. More precisely, for any compact subspace X ⊆ Cm, the abelian group K1(X) classifies essentially normal multioperators with essential Taylor spectrum X up to unitary equivalence; the elements of K1(X) are equivalence classes of C*monomorphisms from C(X) to the algebra of bounded operators on H modulo the ideal of
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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