Matematik Bölümü Seminerleri "Dilations of Positive Semidefinite Kernels Valued in Adjointable Operators of Barrelled VH-Spaces"
Konu : Dilations of Positive Semidefinite Kernels Valued in Adjointable Operators of Barrelled VH-Spaces
Konuşmacı : Serdar Ay (Atılım Üniversitesi)
Tarih: 05.05.2021
Saat: 13:15
Yer: Seminer Zoom programı üzerinden online yapılacaktır. Katılmak isteyenlerin katılım bilgilerini alabilmeleri için huseyinuysal@istanbul.edu.tr adresine mail atmaları gerekmektedir.
Özet: 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.