The non-existence of the Banach lattice structure on the Sobolev spaces and space of functions of bounded variation
Speaker:
Michal Wojciechowski, Polish Academy of Sciences
Date and Time:
Thursday, August 30, 2012 - 1:30pm to 2:10pm
Abstract:
We construct a three dimensional domain D with the property that at least one of the following statements holds true 1) C1 (D) is not isomorphic to C 1 (Ik) for some k > 1, 2) the space Lip (Ik), k > 1, does not have bounded approximation property. Here Ik stands for the k-dimensional cube, C1 (D) is the space of smooth functions with gradient continuously extending to the closure of D, and Lip (Ik) stands for the space of Lipschitz functions on Ik.