[Turkmath:4826] Fwd: [Math-Staff] Atılım University; General Seminar

[Burcu Gulmez Temur]

---------- Forwarded message ---------
From: Demirberk Ünlü <demirberk.unlu at atilim.edu.tr>
Date: Wed, Mar 31, 2021 at 12:25 PM
Subject: [Math-Staff] Atılım University; General Seminar
To: <math-staff at list.atilim.edu.tr>


Dear colleagues,

You are cordially invited to the general seminar organized by the
Department of Mathematics, Atılım University.

Our speaker is * Serdar Ay *(Atılım University).

Date: *April 6,* *2021*

Time: *15:30*

Zoom Meeting ID: *939 794 805 00*

Zoom Meeting Link: https://zoom.us/j/93979480500

Please find the title and the abstract of the talk below.

With kind regards,

On behalf of Seminar Committee.



*Dr. Öğr. Üyesi Demirberk Ünlü*

Matematik Bölümü

Atılım Üniversitesi

T:+90 (312) 586 86 61

F:+90 (312) 586 80 91

A: Kızılçaşar Mahallesi, İncek/Ankara

www.atilim.edu.tr

*Dilations of Positive Semidefinite Kernels Valued in Adjointable Operators
of Barrelled VH-Spaces*

*Abstract*



A VH-space (Vector Hilbert Space in the sense of Loynes) is a complex
complete locally convex space with a with a suitable 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 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. If time permits, we discuss an application of this result as
well.
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