Taiwanese Journal of Mathematics

CONICAL DECOMPOSITION AND VECTOR LATTICES WITH RESPECT TO SEVERAL PREORDERS

R. Baratov and A. Rubinov

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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

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403826

Digital Object Identifier
doi:10.11650/twjm/1500403826

Mathematical Reviews number (MathSciNet)
MR2208268

Zentralblatt MATH identifier
1109.46005

Subjects
Primary: 46B99: None of the above, but in this section 46B42: Banach lattices [See also 46A40, 46B40] 91B54: Special types of economies

Keywords
decomposition mapping Riesz interpolation property Riesz decomposition property vector lattices respect to several preorders

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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