Order convexity and concavity of Lorentz spaces $Λ_{p,w}$, 0 < p < ∞

• Autorzy: Anna Kamińska , Lech Maligranda
• Języki publikacji: EN

Abstrakty

EN

We study order convexity and concavity of quasi-Banach Lorentz spaces $Λ_{p,w}$, where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that $Λ_{p,w}$ 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 $Λ_{p,w}$. We conclude with a characterization of the type and cotype of $Λ_{p,w}$ in the case when $Λ_{p,w}$ is a normable space.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B25: Classical Banach spaces in the general theory
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 3
• Strony: 267-286

Daty

wydano

2004

Twórcy

autor

Anna Kamińska

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

autor

Lech Maligranda

• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Identyfikatory

DOI

10.4064/sm160-3-5