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Abstract M- and Abstract L-Spaces of Polynomials on Banach Lattices

Published online by Cambridge University Press:  13 February 2015

Qingying Bu ,
Gerard Buskes  and
Yongjin Li
Qingying Bu
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, USA (qbu@olemiss.edu; mmbuskes@olemiss.edu)
Gerard Buskes
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, USA (qbu@olemiss.edu; mmbuskes@olemiss.edu)
Yongjin Li
Affiliation:
Department of Mathematics, University of Mississippi, University, MS 38677, USA (qbu@olemiss.edu; mmbuskes@olemiss.edu)
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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.

Keywords

homogeneous polynomialspositive tensor productsAM- and AL-spacesPrimary 46G2546B2846B42
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 3 , October 2015 , pp. 617 - 629
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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