相对于协方差图$η$的解析函数：I.广义Haagerup积与解析关系
Analytic functions relative to a covariance map $η$: I. Generalized Haagerup products and analytic relations
摘要：
推广模弱-* Haagerup张量积，得到了有限vonNeumann代数$B$上完全正的正规（协方差）映射$η$所包含的正规Haagerup张量积的完全逆.我们以这种方式构造对偶算子空间，即使在模扩展Haagerup张量积的情况下也提供了新的例子。这是定义解析函数的矩阵赋范代数的基础，该代数捕获自由半圆形变量与协方差$η$的关系。证明了一类相对于$η$具有有限Fisher信息的非交换随机变量在我们的一类解析函数之间也没有解析关系。
英文摘要：
We generalize module weak-* Haagerup tensor products to obtain complete quotients of normal Haagerup tensor product included in canonical Hilbert spaces associated to completely positive normal (covariance) maps $η$ on a finite von Neumann algebra $B$. We construct in this way dual operator spaces, providing new examples even in the case of module extended Haagerup tensor products. This is the basis for defining a matrix normed algebra of analytic functions that captures the relations of free semicircular variables with covariance $η$. We prove that a class of non-commutative random variables having finite Fisher information relative to $η$ have also no analytic relations among our class of analytic functions.
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