turkmath.org

A VH-space (Vector Hilbert Space in the sense of Loynes) is a complex complete locally convex space with a suitable ordered vector space valued inner product. Examples of VH-spaces include, but is not limited to, the chain of locally Hilbert $C^*$-modules, Hilbert $C^*$-modules and Hilbert Spaces.

In this talk, after a discussion of VH-Spaces with basic properties and some examples, we state a general dilation theorem for positive semidefinite kernels valued in adjointable operators on a barrelled VH-space. We prove that, under barrelledness assumption, a necessary and sufficient condition for the existence of a natural VH-space dilation, or equivalently, a reproducing kernel VH-space representation of the kernel, is satisfied automatically.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1621628614643?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a49a1949-9464-4e2b-861d-221a6985322e%22%7d