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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Order convexity and concavity of Lorentz spaces ${\mit \Lambda }_{p,w}$, $0< p< \infty$

### Tom 160 / 2004

Studia Mathematica 160 (2004), 267-286 MSC: Primary 46E30, 46B20; Secondary 46B42, 46B25. DOI: 10.4064/sm160-3-5

#### Streszczenie

We study order convexity and concavity of quasi-Banach Lorentz spaces ${\mit \Lambda }_{p,w}$, where $0< p< \infty$ and $w$ is a locally integrable positive weight function. We show first that ${\mit \Lambda }_{p,w}$ contains an order isomorphic copy of $l^p$. We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for ${\mit \Lambda }_{p,w}$. We conclude with a characterization of the type and cotype of ${\mit \Lambda }_{p,w}$ in the case when ${\mit \Lambda }_{p,w}$ is a normable space.

#### Autorzy

• Anna KamińskaDepartment of Mathematical Sciences
The University of Memphis
Memphis, TN 38152, U.S.A.
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