# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Complex extreme points in Marcinkiewicz spaces

Positivity, Volume 19 (1) – May 14, 2014
15 pages

/lp/springer_journal/complex-extreme-points-in-marcinkiewicz-spaces-Ikeo7LDh9W
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0287-3
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

PositivitySpringer Journals

Published: May 14, 2014

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations