Dominated n-linear operators with respect to a system of n bounded linear operators. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Popa, Dumitru
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 6(2017)
• Page Start: 1097
• Page End: 1107
• Publication Date: 2017-06-03
• Subjects: p-summing operators -- Ky Fan lemma -- dominated operators -- operators on spaces of vector valued continuous functions; Primary: 47L20 -- 46G25 -- 47H60 -- Secondary: 47B10 -- 46G10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1228814
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : For a bounded n -linear operator, , ..., a system of n bounded linear operators and we introduce the concept of Grothendieck–Pietsch -dominated operator. We use Ky-FanLemma to prove a characterization of -dominated operators. As application we characterize -dominated operators on . We show that similar ideas can be used to obtain a new characterization of the dominated operators in the sense of N. Dinculeanu and, as an application, we prove an extension of a result of A. Defant and M. Junge.