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Tuesday, 8 April 2025 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Eva Pernecká, ČVUT<br />
Title: De Leeuw representation of functionals in Lipschitz-free spaces
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Abstract <br />
<p> At present, no general representation theorem for duals of spaces of </p><p>Lipschitz functions over a pointed metric space is known. A useful </p><p>substitute is provided by a construction due to K. de Leeuw from the </p><p>1960s, which allows us to view functionals on spaces of Lipschitz </p><p>functions as Radon measures integrating the incremental quotients of </p><p>functions. </p><p><br></p><p> We will focus on functionals from the canonical predual of the space of </p><p>Lipschitz functions, the Lipschitz-free space. We will discuss the </p><p>existence of ``nice'' representing measures for such functionals and </p><p>present some applications to the isometric theory of Lipschitz-free </p><p>spaces. In particular, we will show that a Choquet-like theory for De </p><p>Leeuw representations, recently developed by R. J. Smith, leads to an </p><p>``inner regularity'' result for elements of Lipschitz-free spaces and </p><p>the characterisation of the extreme points of their unit balls. </p><p><br></p><p> The talk will be based on joint work with Ramón J. Aliaga (Universitat </p><p>Politècnica de València) and Richard J. Smith (University College </p><p>Dublin). </p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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