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Dear list members,<br><br>You are most cordially invited to the <span class="gmail-il">seminar</span> organized by the Department of Mathematics Yeditepe University.<div><br></div><div></div>Title: Dilations of positive semidefinite kernels valued in operators of barrelled VH-spaces<br><div class="gmail_quote"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div><br>Speaker: Serdal Ay (Bilkent University)<br><br>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.<br> <br> 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.</div><div><br></div><div>Date: Friday, May 8, 2020<br></div><div>Time: 13:00</div><div>Google Meet Code: 7tpmathseminars</div><div><br></div><div><br></div><div> <span>P.S.</span>: If you are not within the Yeditepe University Network and willing to join the <span class="gmail-il">seminar</span>, please contact me before the <span class="gmail-il">seminar</span> time so that I can send an invitation link.
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