On the extreme points and strongly extreme points in Köther-Bochner spaces

On the Extreme Points and Strongly Extreme Points in Köthe–bochner Spaces

We give the necessary conditions of extreme points and strongly extreme points in the unit ball of Köthe–Bochner spaces. The conditions have been shown to be sufficient earlier.

Extreme points of the unit cell Lebesgue-Bochner function spaces

Extreme Points and Rotundity in Musielak-Orlicz-Bochner Function Spaces Endowed with Orlicz Norm

and Applied Analysis 3 Put LM X { u ∈ XT : ρM λu < ∞ for some λ > 0 } . 1.5 Then the Musielak-Orlicz-Bochner function space ‖u‖ inf k>0 1 k [ 1 ρM ku ] 1.6 is Banach space. If X R, LM R is said to be Musielak-Orlicz function space. Set K u { k > 0 : 1 k ( 1 ρM ku ) ‖u‖ } . 1.7 In particular, the set K u can be nonempty. To show that, we give a proposition. Proposition 1.1. If limu→∞ M t, u /u ∞...

Extreme points of the unit cell in Lebesgue-Bochner functions spaces

Concerning weak ∗ - extreme points

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.