GEOMETRIC CONSTANTS OF DISCRETE MORREY SPACES
Geometric constantswhichquantifyvariousgeometricfeaturesofBanachspaces often playrolesinfunctionalanalysis.Inthisthesis,thestudyofgeometric constants willfocusonthe n-th Jamesconstantand n-th VonNeumann-Jordan constant. Theseconstantscanmeasuretheroundnessofthe n-dimensional unit sphere inaBanac...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/55022 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
|---|