Local structure of Riesz valued sequence spaces defined by an order -function. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Herawati, E.; Supama, ; Mursaleen, M.
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 3(2017)
• Page Start: 545
• Page End: 554
• Publication Date: 2017-03-04
• Subjects: Order-function -- -order continuous -- strictly monotonic -- uniformly monotonic -- locally monotonic; Primary: 39B82 -- Secondary: 44B20 -- 46C05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1194803
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : For a Riesz space E, we introduce E -valued sequence spaces generated by an order -function. It is proved that these spaces equipped with a Luxemburg norm are ideal Banach lattices. We also determine necessary and sufficient conditions so that the Luxemburg norm on these spaces has the -order continuous property. Finally, we present some criteria for strictly monotonicity, uniformly monotonicity and locally monotonicity of the spaces.