Taiwanese Journal of Mathematics

LOCAL $\Delta_2^E$ CONDITION IN GENERALIZED CALDERÓN-LOZANOVSKĬ SPACES

Pawel Kolwicz and Agata Panfil

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Abstract

First we present the local $\Delta_2^E$ condition in generalized Calderón-Lozanovskiĭ spaces $E_\varphi$ and we discuss the relationships between the local and the global $\Delta_2^E$ condition in such spaces. We also give a full characterisation for a point of $B(E_\varphi)$ to have an order continuous norm. Then we apply the main result to particular spaces, i.e. Calderón-Lozanovskiĭ spaces and Orlicz-Lorentz spaces.

Article information

Source
Taiwanese J. Math., Volume 16, Number 1 (2012), 259-282.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406540

Digital Object Identifier
doi:10.11650/twjm/1500406540

Mathematical Reviews number (MathSciNet)
MR2887864

Zentralblatt MATH identifier
1244.46013

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B20: Geometry and structure of normed linear spaces 46B42: Banach lattices [See also 46A40, 46B40] 46B45: Banach sequence spaces [See also 46A45] 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]

Keywords
Köthe spaces generalized Calderón-Lozanovskiĭ spaces Orlicz-Lorentz spaces global and local $\Delta_2^E$ condition points of order continuous norm

Citation

Kolwicz, Pawel; Panfil, Agata. LOCAL $\Delta_2^E$ CONDITION IN GENERALIZED CALDERÓN-LOZANOVSKĬ SPACES. Taiwanese J. Math. 16 (2012), no. 1, 259--282. doi:10.11650/twjm/1500406540. https://projecteuclid.org/euclid.twjm/1500406540


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