Abstract
The classic Banach-Mazur theorem says that C[0,1] is a universal (isometrically) space for all the separable Banach spaces X. However, can we impose some extra regularity to the continuous functions representing the elements of X? We will study this problem in a more general frame with functions on a compact Hausdorff space K and regularity with respect to to a lower semicontinuous metric d defined on K. The results will tell us that, in general, the existence of an isometric copy of a separable Banach space X into C(K) made of functions which are Lipschitz with respect to d, imposes severe restrictions to both X and K.
Speaker: Prof. Matias Raja Bano | Department of Mathematics | University of Murcia
Chairperson: Dr. Ralph Agyei Twum | Department of Mathematics | University of Ghana
Meeting ID: 336 861 734 014 115 | Passcode: fS6o9UX7 | Teams: Link
All are cordially invited.