Extension Theorems and the Riesz Decomposition Property

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2003 English Publisher:Springer Science and Business Media LLCJournal:Positivity, volume 7, pages 87-93 (issn: 1385-1292, eissn: 1572-9281,

Copyright policy )

Authors: Dăneţ, Nicolae; Dăneţ, Rodica-Mihaela;

doi: 10.1023/a:1025883207672

Extension Theorems and the Riesz Decomposition Property

- Summary
- Subjects
- Metrics

Abstract

This paper is a survey of the contributions by the authors and N.-C. Wong, concerning the following two problems: (a) the Riesz decomposition property for spaces of regular operators; (b) the extension of positive operators. The original results appeared in [\textit{N. Dăneţ}, Proc. Am. Math. Soc. 129, 539--542 (2001; Zbl 0974.47033) and Suppl. Rend. Circ. Mat. Palermo, II. Ser. 68(1), 373--380 (2002; Zbl 1029.47023); \textit{R.-M. Dăneţ} and \textit{N.-C. Wong}, Taiwanese J. Math. 6, 241--246 (2002; Zbl 1052.47030) and Suppl. Rend. Circ. Mat. Palermo, II. Ser. 68(1), 381--387 (2002; Zbl 1041.47016)].

Related Organizations

Technical University of Civil Engineering of Bucharest
Romania

Keywords

Banach lattices, ordered vector space, Research exposition (monographs, survey articles) pertaining to operator theory, Hahn-Banach theorem, Linear operators on ordered spaces, Positive linear operators and order-bounded operators, Theorems of Hahn-Banach type; extension and lifting of functionals and operators, regular operator

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	4
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average