Traced tensor norms and multiple summing multilinear operators. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Rueda, P.; Sánchez-Pérez, E. A.; Tallab, A.
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 4(2017)
• Page Start: 768
• Page End: 786
• Publication Date: 2017-04-03
• Subjects: Multilinear operator -- summing operator -- multiple summing operator -- -summing operator -- tensor norm; 47L22 -- 46A32 -- 47B10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1202186
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p -summing bilinear operators, ( p, q )-factorable linear operators, -summing linear operators and absolutely p -summing linear operators, providing a characterization of this later class whenever the absolutely p -summing linear operators take values in an -space.