Tuesday 30/10, Marek Cúth

kubis at math.cas.cz kubis at math.cas.cz
Fri Oct 26 10:00:02 CEST 2018


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 Tuesday 30th October, 10:00am 
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 Speaker:Marek Cúth, Charles University, Faculty of Mathematics and Physics
 Title: Lipschitz free p-spaces over quasimetric spaces

 Abstract  
I will talk about our paper in preparation with F. Albiac, J. L. Ansorena and M. Doucha, where we study Lipschitz free p-spaces over quasimetric spaces. Those spaces were used in a paper by F. Albiac and N. Kalton to build  examples for each $0<p<1$ of two separable $p$-Banach spaces which are Lipschitz-isomorphic but fail to be linearly isomorphic. However, even though we have the nice application of Lipschitz free $p$-spaces mentioned above, the structure of those spaces has not been investigated ever since. Our goal was to fill this gap in the theory and encourage further research in this direction. In my talk I will try to summarize some basic observations and hopefully I will keep some not negligible time to talk about one of our main results: there is a (p)-metric space M and its subspace N such that the canonical mapping from F_p(N) to F_p(M) is NOT an isometry. This solves a problem proposed by F. Albiac and N. Kalton. We do not know whether it is possible 
 to build such an example that the mapping is not even an isomorphism.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .



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