## Taiwanese Journal of Mathematics

### CONICAL DECOMPOSITION AND VECTOR LATTICES WITH RESPECT TO SEVERAL PREORDERS

#### Abstract

The decomposition set-valued mapping in a Banach space $E$ with cones $K_i$, $i = 1, \ldots, n$ describes all decompositions of a given element on addends, such that addend $i$ belongs to the $i$-th cone. We examine the decomposition mapping and its dual.

We study conditions that provide the additivity of the decomposition mapping. For this purpose we introduce and study the Riesz interpolation property and lattice properties of spaces with respect to several preorders. The notion of 2-vector lattice is introduced and studied. Theorems that establish the relationship between the Riesz interpolation property and lattice properties of the dual spaces are given.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 2 (2006), 265-298.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403826

Digital Object Identifier
doi:10.11650/twjm/1500403826

Mathematical Reviews number (MathSciNet)
MR2208268

Zentralblatt MATH identifier
1109.46005

#### Citation

Baratov, R.; Rubinov, A. CONICAL DECOMPOSITION AND VECTOR LATTICES WITH RESPECT TO SEVERAL PREORDERS. Taiwanese J. Math. 10 (2006), no. 2, 265--298. doi:10.11650/twjm/1500403826. https://projecteuclid.org/euclid.twjm/1500403826

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