[Turkmath:4460] Seminar on May 8, 2020 via Google Meet - Department of Mathematics

[Mehmet Akif Erdal]

 Dear list members,

You are most cordially invited to the seminar organized by the Department
of Mathematics Yeditepe University.

Title: Dilations of positive semidefinite kernels valued in operators of
barrelled VH-spaces

Speaker: Serdal Ay (Bilkent University)

Abstract: A VH-space (Vector Hilbert Space in the sense of Loynes) is a
complex complete locally convex space with a topologically ordered
$*$-space valued inner product. Examples of VH-spaces include the chain of
locally Hilbert $C^*$-modules, Hilbert $C^*$-modules and Hilbert Spaces.

In this talk, after a brief discussion of VH-Spaces with examples and basic
properties, 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.

Date: Friday, May 8, 2020
Time: 13:00
Google Meet Code: 7tpmathseminars


 P.S.: If you are not within the Yeditepe University Network and willing to
join the seminar, please contact me before the seminar time so that I can
send an invitation link.
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