Banach Journal of Mathematical Analysis

Note on extreme points in Marcinkiewicz function spaces

Anna Kaminska and Anca M. Parrish

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We show that the unit ball of the subspace $M_W^0$ of ordered continuous elements of $M_W$ has no extreme points, where $M_W$ is the Marcinkiewicz function space generated by a decreasing weight function $w$ over the interval $(0,\infty)$ and $W(t) = \int_0^tw$, $t\in(0,\infty)$. We also present here a proof of the fact that a function $f$ in the unit ball of $M_W$ is an extreme point if and only if $f^*=w$.

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Banach J. Math. Anal., Volume 4, Number 1 (2010), 1-12.

First available in Project Euclid: 27 April 2010

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Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Marcinkiewicz function spaces extreme points


Kaminska , Anna; Parrish , Anca M. Note on extreme points in Marcinkiewicz function spaces. Banach J. Math. Anal. 4 (2010), no. 1, 1--12. doi:10.15352/bjma/1272374667.

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