再生核范畴中的泛对象
Universal objects in categories of reproducing kernels
摘要：
我们继续我们以前的调查广义再生核，与复杂的几何$C^*$ -代数表示，通过查看它们作为一个适当的类别的对象。因此，再生$(-*)$ -核与向量丛的截面的相关希尔伯特空间之间的对应关系被制成函子。我们构造再生$(-*)$ -内核与普适性的操作拉回。我们证明了完全正映射可以被看作是希尔伯特空间$\ell^2({\mathbb N})$的格拉斯曼流形上重言丛上的泛映射的拉回。
英文摘要：
We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of $C^*$- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence between reproducing $(-*)$-kernels and the associated Hilbert spaces of sections of vector bundles is made into a functor. We construct reproducing $(-*)$-kernels with universality properties with respect to the operation of pull-back. We show how completely positive maps can be regarded as pull-backs of universal ones linked to the tautological bundle over the Grassmann manifold of the Hilbert space $\ell^2({\mathbb N})$.
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