Abstract M- and Abstract L-Spaces of Polynomials on Banach Lattices. Issue 2 (October 2015)

• Record Type: Journal Article
• Authors: Bu, Qingying; Buskes, Gerard; Li, Yongjin
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 58:Issue 2(2015)
• Page Start: 617
• Page End: 629
• Publication Date: 2015-10
• Subjects: homogeneous polynomials, -- positive tensor products, -- AM- and AL-spaces; Primary 46G25, -- 46B28, -- 46B42; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091514000297
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: In this paper we use the norm of bounded variation to study multilinear operators and polynomials on Banach lattices. As a result, we obtain when all continuous multilinear operators and polynomials on Banach lattices are regular. We also provide new abstract M- and abstract L-spaces of multilinear operators and polynomials and generalize all the results by Grecu and Ryan, from Banach lattices with an unconditional basis to all Banach lattices.