GEOMETRIC CONSTANTS OF DISCRETE MORREY SPACES - Adam
Geometric constantswhichquantifyvariousgeometricfeaturesofBanachspaces often playrolesinfunctionalanalysis.Inthisthesis,thestudyofgeometric constants willfocusonthe n-th Jamesconstantand n-th VonNeumann-Jordan constant. Theseconstantscanmeasuretheroundnessofthe n-dimensional unit sphere inaBanachspaceanddetermineuniformlynon-`1 n property ofthatBanach space. Morespecifically,wewillcomputethetwoconstants’valuefordiscrete Morreyspace.Inthisthesis,wewillshowthat C(n) NJ (`p q (Zd)) = C(n) J (`p q (Zd)) = n where 1 p <q< 1. ThisresultshowsthatdiscreteMorreyspaceisnot uniformly non-`1 n and the n-dimensional unitsphereindiscreteMorreyspaceisnot round atall.TheseresultsalsoshowthatthediscreteMorreyspaceisnotuniformly n-convex.Furthermore,thegeometricbehaviorofdiscreteMorreyspaceissimilar to `1 and `1.