Complex extreme points in Marcinkiewicz spaces

Complex extreme points in Marcinkiewicz spaces In this paper we characterize complex extreme points in Marcinkiewicz spaces $$M_W$$ M W , with a non-increasing weight $$w$$ w . We showed that $$f \in S_{M_W}$$ f ∈ S M W is a complex extreme point of the unit ball $$B_{M_W}$$ B M W if and only if $$\liminf _{t\rightarrow \infty }\{\int _0^t w(s)\,ds-\int _0^t f(s)\,ds\}=0$$ lim inf t → ∞ { ∫ 0 t w ( s ) d s - ∫ 0 t f ( s ) d s } = 0 . Moreover, we proved that the unit ball is the weak star closure of its complex extreme points. Positivity Springer Journals

Complex extreme points in Marcinkiewicz spaces

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Springer Basel
Copyright © 2014 by Springer Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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