论文标题
乘数测试和乘数代数的亚均匀性
Multiplier tests and subhomogeneity of multiplier algebras
论文作者
论文摘要
复制内核希尔伯特空间的乘数可以以$ n \ times n $矩阵类似于经典的选拔矩阵的阳性来表征。我们研究了在哪个繁殖内核希尔伯特空间，可以考虑有界尺寸$ n $的矩阵。我们将此问题与非频道操作员代数的亚均匀性的概念联系起来。我们的主要结果表明，许多分析功能的希尔伯特空间的乘数代数，例如Dirichlet空间和Drury-Arveson空间，并不是均匀的，因此必须测试任意较大矩阵大小$ n $的选择的选拔矩阵。为了处理Drury-Arveson空间，我们表明在圆盘上某些加权Dirichlet空间的乘数代数完全嵌入了Drury-Arveson空间的乘数代数中。
Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of bounded size $n$. We connect this problem to the notion of subhomogeneity of non-selfadjoint operator algebras. Our main results show that multiplier algebras of many Hilbert spaces of analytic functions, such as the Dirichlet space and the Drury-Arveson space, are not subhomogeneous, and hence one has to test Pick matrices of arbitrarily large matrix size $n$. To treat the Drury-Arveson space, we show that multiplier algebras of certain weighted Dirichlet spaces on the disc embed completely isometrically into the multiplier algebra of the Drury-Arveson space.
