İstanbul Analysis Seminars

Dilation theory of invariant kernels valued in continuously adjointable operators of VH-spaces
Serdar Ay
Bilkent University, Turkey
Özet : We consider positive semidefinite kernels that are invariant under an action of a $*$-semigroup and valued in the continuous and continuously adjointable operators of VH (Vector Hilbert)-spaces in the sense of Loynes. The main theorem gives two necessary and sufficient boundedness conditions for the existence of an invariant Kolmogorov decomposition of the kernel, or equivalently, $*$-representations of the $*$-semigroup on a reproducing kernel VH-space. We discuss several cases in which the latter boundedness condition follows automatically. This is a joint work with A. Gheondea.
 Tarih : 22.04.2016 Saat : 15:40 Yer : Sabancı University, Karaköy Communication Center, Bankalar Caddesi 2, Karaköy Dil : English