The natural rearrangement invariant structure on tensor products

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article

Fernandez-Gonzalez, C.²  Palazuelos, C.¹  Perez-Garcia, D.¹ 

[1] Univ Complutense Madrid, Dept Anal Matemat, Fac Matemat, E-28040 Madrid, Spain

[2] Univ Complutense Madrid, Dept Algebra, Fac Matemat, E-28040 Madrid, Spain

关键词: crossnorms in tensor product;    rearrangement invariant spaces;    Lp spaces;   

DOI  :  10.1016/j.jmaa.2008.01.016

来源: Elsevier

【 摘 要 】

We prove that the only rearrangement invariant (r.i.) spaces for which there exists a crossnorm verifying that the tensor product of these spaces preserves the natural r.i. space structure, in the sense that it makes the multiplication operator B a topological isomorphism, are the Lp spaces. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free